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Feature selection has been considered as an effective method to solve imbalanced classification problems. It can be formulated as a multiobjective optimization problem (MOP) aiming to find a small feature subset while achieving a high classification accuracy. With traditional MOP, the focus is on deriving an optimal solution (i.e., a feature subset), while ignoring the diversity in solution space (e.g., there could exist multiple feature subsets achieving the same accuracy). Providing more options for feature selection would be beneficial since some features can be more difficult to obtain than others. In this work, we treat feature selection as a multimodal MOP (MMOP) whose goals are to find an excellent Pareto front in objective space and as many equivalent Pareto optimal solutions (feature subsets) as possible in feature space. Note that though several multimodal multiobjective evolutionary algorithms (MMEAs) have been proposed, their use of a convergence-first selection criterion could cause the loss of solution diversity in an objective and feature space. To address the issue, a novel competition-driven mechanism is designed to assist the existing multimodal MMEAs in locating more equivalent feature subsets and a desired Pareto front. The effectiveness of the proposed mechanism is first verified on all 22 MMOPs from CEC2019. Then, the proposed method is applied to feature selection in imbalanced classification problems and a real-world application, i.e., credit card fraud detection. Experimental results show that the proposed mechanism can not only provide more equivalent feature subsets but also improve classification accuracy. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

Dynamical systems coupled in the form of a complex networks have been exploited for modeling numerous real-world distributed systems. Due to the decentralized nature of dynamical networks, and inaccessibility or high control cost, in some applications, it is desired to employ pinning control techniques. A natural question that comes to mind is how one can select the proper pinned nodes and their feedback gains, (i.e., the performance metrics) to optimize the convergence rate to the homogeneous stationary state (i.e., the performance index) while the total pinning cost is kept below a given limit. This optimization problem has been converted into a semidefinite programming problem, and the optimal feedback gains have been derived analytically. Based on these results, for a given set of pinned nodes, an algorithm for determining the optimal feedback gains has been developed. Furthermore, it is shown that the edges between the pinned nodes do not impact the optimal results, and adding an edge between free nodes or between free and pinned nodes modifies the optimal convergence rate in nondecreasing order. Based on the derived analytical results, several interesting properties have been discovered. For symmetric networks, the nodes within a vertex orbit have the same optimal feedback gains, which are independent of the edges within each vertex orbit. For a number of topologies, closed-form formulas are provided for the optimal results. For a network of Chua systems, the impact of cut number is illustrated by comparing the optimal results for different topologies. [ABSTRACT FROM AUTHOR]

Human-on-the-loop (HOTL) system is regarded as a promising technology to allow autonomous underwater vehicle (AUV) to track the most adequate target point as soon as possible. However, the unique characteristics of the underwater environment make it challenging to perform the tracking task. This article is concerned with a finite-time tracking control issue for AUV, subjected to unavailable velocity signals in the measurement side and uncertain model parameters in physical side. A HOTL system, including operator, buoys, AUV and sensors, is first provided to construct a cooperative tracking network. For such system, operator in surface control center decides the tracking mission based on all available data. Then, a buoy-assisted localization estimator is utilized by AUV to acquire its position, through which a fast terminal sliding mode observer is developed to estimate the velocity of AUV in finite time. With the estimated velocity information, an adaptive-nonsingular fast terminal sliding mode tracking controller is designed to drive AUV to the target point in finite time. For the proposed velocity observer and tracking controller, the signum and differential functions are employed together to improve the convergence speed and reduce the chattering. Besides that, the proposed solution can not only guarantee finite-time velocity observation, but also achieve finite-time tracking control. Finally, simulation and experimental results are both presented to verify the effectiveness. [ABSTRACT FROM AUTHOR]

The work has devised a novel fixed-time control scheme for a class of nonlinear systems with output constraints. Two distinctive features are incorporated into the gained results. One is that the upper bound of settling time for the closed-loop system can be estimated without dependence on system initial states, and hence, can be acquired arbitrarily small through tuning control design parameters. The other is that the output constraint can be handled by means of a barrier Lyapunov function (BLF). Via the BLF and the backstepping-like technique, a fixed-time controller, which can cope with a type of nonlinear systems concurrently with and without output constraints, is systematically built. The rigorous analysis on the strength of the Lyapunov theory is given to show that the investigated system under the proposed controller is fixed-time stable, and the violation of a preset output constraint is averted. The case studies of a series elastic actuator system are offered to substantiate the derived theoretical results. [ABSTRACT FROM AUTHOR]

A data-driven strategy to estimate the optimal feedback and the value function in an infinite-horizon, continuous-time, linear-quadratic optimal control problem for an unknown system is proposed. The method permits the construction of the optimal policy without any knowledge of the model, without requiring that the time derivatives of the state are available for the design, and without even assuming that an initial stabilizing feedback policy is available. Two alternative architectures are discussed: the first scheme revolves around the periodic computation of some matrix inversions involving the Q-function, whereas the second approach relies on a purely continuous-time implementation of some dynamic systems whose trajectories are uniformly attracted by the solutions to the above algebraic equations. Interestingly, the proposed strategy essentially constitutes a (direct) data-driven implementation of the celebrated Kleinman algorithm, hence subsuming the particularly appealing features of the latter, such as quadratic monotone convergence to the optimal solution. The theory is then validated by the means of practically motivated applications. [ABSTRACT FROM AUTHOR]

In this article, we consider a class of decentralized nonsmooth composite optimization problems over undirected graphs. The global optimization problem is to minimize the sum of local objective functions consisting of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which contains a bounded linear operator. The goal is to solve the global optimization problem through decentralized computation and communication over a network of agents without a central coordinator. Through using triple proximal splitting operators to deal with the nonsmooth terms, we come up with a novel decentralized algorithm with uncoordinated stepsizes, where the stepsizes with independent upper bounds are also distributed for agents or edges over the communication network. Furthermore, we establish the sublinear convergence rate for the proposed algorithm in terms of the first-order optimality residual in a nonergodic sense. Simulation experiments on a constrained quadratic programming problem and an optimal load-sharing problem are carried out to verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Multiobjective optimization evolutionary algorithms (MOEAs) have received significant achievements in recent years. However, they encounter many difficulties in dealing with many-objective optimization problems (MaOPs) due to the weak selection pressure. One possible way to improve the ability of MOEAs for these MaOPs is to balance the convergence and diversity in the high-dimensional objective space. Based on this consideration, this article proposes a novel generic two-stage (TS) framework for MaOPs. The entire evolutionary search process is divided into two stages: in the first stage, a new subregion dominance and a modified subregion density-based mating selection mainly purse the convergence and in the second stage, a novel level-based Pareto dominance cooperates with the traditional Pareto dominance that mainly promotes diversity. Integrated into NSGA-II, the TS NSGA-II, referred to as TS-NSGA-II, is proposed. To extensively evaluate the performance of our approach, 29 benchmark problems were used as the test suite. The experimental results demonstrate our approach obtained superior or competitive performance compared with eight state-of-the-art many-objective optimization evolutionary algorithms. To study its generality, the proposed TS strategy was also combined with four other advanced methods for MaOPs. The results show that it can also improve the performance of these four methods in terms of convergence and diversity. [ABSTRACT FROM AUTHOR]

Up to date, the existing methods for nonlinear optimization with time-dependent parameters can be classified into two types: 1) static methods are capable of handling inequality constraints but may generate large lagging errors in the solution of the intrinsically time-dependent constrained nonlinear optimization (TDCNO) problem due to the hypothesis of short-time invariance and 2) time-variant methods, e.g., zeroing neural networks, are able to remedy the lagging error but fail to solve the TDCNO problem under inequality constraints. To resolve this contradiction, a noise-suppressing neural dynamics (NSND) model is proposed to solve the TDCNO problem subject to both equality and inequality constraints via the nonlinear complementary problem (NCP) function. The proposed method allows inequality constraints for unknown variables, removes the short-time invariance hypothesis, and further eliminates lagging errors during the solving process in the presence of noises. Besides, the rapid convergence, global stability, and noise processing of the NSND model are verified by the theoretical analyses. Simulation results of illustrative examples, including dimensionality reduction on principal component analyses (PCA) and a robot motion control, show that the NSND model outperforms the existing models for the TDCNO problem. [ABSTRACT FROM AUTHOR]

Undirected, high-dimension and sparse (SHiDS) networks which are often encountered in industrial applications usually contain numerous useful information; thus, it is practically important to develop effective collaborative filtering methods to rigidly extract the latent information. In order to improve the performance of nonnegative latent factor (NLF) models based on the double factorization while reducing the computation burden of NLF models in terms of the triple factorization (TF) technique, a novel symmetric NLF (SNLF) model, i.e., TF-like SNLF model, is proposed in this article. A latent factor (LF) matrix that reflects the relationship of items is introduced into the objective function so as to offer more freedom for solutions. Then, a fixed weighting matrix designed by sensitivity experiments is used to replace the aforementioned LF matrix dependent on the update, which greatly helps save the time cost without sacrificing any accuracy. Furthermore, the alteration direction (ADI) method is adopted to design the algorithm, which effectively helps reduce the occurrence of the local minimum while guaranteeing convergence. Finally, experimental results on four real industrial data sets demonstrate that the proposed TF-like SNLF model makes a good compromise between the model performance and the time efficiency. [ABSTRACT FROM AUTHOR]

Competitive swarm optimizers (CSOs) have shown very promising search efficiency in large-scale decision space. However, they face difficulties when solving large-scale multi-/many-objective optimization problems (LMOPs), as their winner particles are selected by random pairwise competition based on only a single evaluation criterion, which does not provide diverse guidance for LMOPs. To alleviate this issue, this article proposes a comprehensive competitive learning (CCL) strategy for CSOs using three competition mechanisms to guide the particle search. Specifically, environmental competition classifies winner and loser particles from the swarm, while cognitive competition and social competition select one winner particle as the cognitive component and the social component, respectively, to guide the search for loser particles. This competitive learning strategy aims to enhance the search capability of loser particles and provides diverse search directions for solving LMOPs. When compared with eight competitive optimizers, the experimental results validate the high efficiency and effectiveness of our method in solving nine LMOPs with 2–10 objectives and 100–5000 variables. [ABSTRACT FROM AUTHOR]

To realize the robust control of multirotor unmanned aerial vehicle (UAV) systems, adaptive multilayer neural dynamics (AMND) controllers are proposed and analyzed. The proposed AMND controllers with the strong anti-perturbation property can drive multirotor UAVs to track time-varying tasks and deal with parameter uncertainty problems. First, the design method of the general multilayer neural dynamics (MLND) controllers is introduced and analyzed. Second, based on the design method, the attitude angles, height, and position controllers of a UAV system are designed. Third, according to the adaptive control theory, a novel AMND controller is designed, which can self-tune the parameters of the UAV. Finally, the proposed AMND method applies to a real-world hexrotor UAV system to illustrate its reliability. Mathematical analysis, computer simulations, and experiments verify the reliability, stability, and effectiveness of the proposed controllers which are used to track time-varying tasks. [ABSTRACT FROM AUTHOR]

This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study. [ABSTRACT FROM AUTHOR]

An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified. [ABSTRACT FROM AUTHOR]

Zeroing neural network (ZNN), an effective method for tracking solutions of dynamic equations, has been developed and improved by various strategies, typically the application of nonlinear activation functions (AFs) and varying parameters (VPs). Unlike VPs, AFs applied in ZNN models act directly on real-time error. The processing unit of v needs to obtain neural state in real time. In the implementation process, highly nonlinear AFs become an important cause of time delays, which eventually leads to instability and oscillation. However, most studies focus on exploring new theoretically valid AFs to improve performance of ZNNs, while ignoring the adverse effects of highly nonlinear AFs. The nonlinearity of AFs requires us fully consider time-delay tolerance of ZNNs using nonlinear AFs, so as to ensure that the model is not unstable even when disturbed by time delays. In this work, delay-perturbed generalized ZNN (DP-GZNN) is proposed to investigate time-delay tolerance of generalized ZNN (G-ZNN) in solving dynamic Lyapunov equation. Considering the nonlinearity of AFs, two delay terms are elegantly added to G-ZNN and DP-GZNN is then derived. After rigorous mathematical derivations, sufficient conditions in a linear matrix inequality (LMI) manner are presented for global convergence of DP-GZNN. Through rich numerical experiments, hyperparameters involved in the analysis process are discussed in detail. Comparative simulations are also conducted to compare the ability of different ZNN models to resist time delays. It is worth to mention that this is the first time to consider the ability of G-ZNN to resist discrete and distributed time delays. [ABSTRACT FROM AUTHOR]

Many complex nonlinear optimization or control issues can be transformed into the solving of time-varying nonlinear equations (TVNEs), playing a fundamental role in the control and management of complex systems. As a result, a robust and high-precision online solution method is significant for TVNE. However, there are three main challenges for handling TVNE via the existing methods: First, short-time invariance assumption frequently leveraged in the existing methods leads to lagging errors that are difficult to eliminate. Second, it is difficult in dealing with unknown noise disturbance during the solution process, which causes low solution accuracy or solution failure. Third, existing continuous-time methods are hard to be implemented on digital equipments. In this article, an anti-noise discrete-time neural dynamics (DTND) is designed and studied to overcome the above issues systematically. The theoretical analysis and numerical simulations demonstrate that the proposed model effectively eliminates the lagging errors and achieves the accurate solution of the TVNE in a noisy environment. Moreover, to verify the superior numerical computational property of the DTND model, the intention recognition of lower limbs is explored from the artificial systems, computational experiments, and parallel execution (ACP) framework. Specifically, a nonlinear artificial dynamic system (NADS) concerning the human surface electromyogram (sEMG) signals and joint information is established, which performs in parallel with the actual human lower limb physical experiments. Simulation results illustrate that, within the acceptable range of the digital computer, the controller designed by the DTND model can well guide the NADS to accurately recognize the motion intention of the human lower limb. [ABSTRACT FROM AUTHOR]

In this article, the distributed finite-time and fixed-time optimization problems are investigated by adopting the zero-gradient-sum (ZGS) framework in multiagent systems. Specifically, when the local convex functions are nonquadratic, a basic optimization protocol is proposed to obtain a finite-time convergence, such that the networked system can cooperatively seek the optimal solution of the global objective, the sum of local objective, in a limited time. By utilizing the property of quadratic functions, a reduced algorithm can remove the dependence of initial conditions in the estimation of the upper bound of settling time and achieve a fixed-time result. Besides, the problem with time-varying topologies is studied by introducing a modified algorithm with an artificial potential function to preserve the network connectivity. Finally, the validity of the protocols is demonstrated via some example simulations. [ABSTRACT FROM AUTHOR]

In this article, the leader-following exponential consensus problem of fractional-order descriptor multiagent systems (FOD-MASs) with event-triggered control (ETC) protocol is investigated, which includes integer-order descriptor multiagent systems as the special case. Two classes of control schemes and the corresponding event-triggered conditions are presented, respectively. First, a distributed state feedback ETC protocol is developed to reach the leader-following exponential consensus. The leader-following exponential consensus is achieved in the sense of the Mittag-Leffler stability of fractional-order systems. Second, when full-state measurements are not available, a novel observer-type output feedback ETC strategy with some desirable characteristics is provided. For two distributed ETC protocols, consensus conditions are derived and convergence rate of the system can be adjusted. Also, the integral inequality is applied to get the fact that Zeno behavior is excluded, which verifies the feasibility of ETC schemes. Finally, the effectiveness of conclusions is demonstrated by the examples. [ABSTRACT FROM AUTHOR]

For distributed estimation arising in the nonlinear least squares (NLLSs) problems over adaptive networks, where every node has the abilities of data processing and learning, only the incomplete local data are exploited by the traditional noncooperative method, thereby resulting in the degradation on estimation performance. In this article, a cooperative diffusion strategy is proposed by using a Gauss–Newton (GN) method in order to fully utilize the diversity of temporal–spatial data on local updates. The proposed algorithm includes two steps, i.e., aggregate then update (ATU), where the aggregating step collects in real time the global information instead of local information due to the diffusion strategy, and the updating step implements the local GN iteration. The resulting ATU diffusion algorithm is a distributed and cooperative system without any increase on communication cost, as compared with the noncooperative version. Based on the detailed convergence analysis for ATU, which is fundamental to the promotion of this algorithm, the sufficient conditions for convergence are derived and the evidences of faster convergence than the noncooperative version are provided. The simulation results confirm the obtained theoretical derivations by applying the ATU algorithm to an NLLS-based target localization problem and show the cooperation gains in many aspects, such as the convergence rate, steady-state accuracy, and robustness to noisy range, step size, node, and link failures. [ABSTRACT FROM AUTHOR]

The learning control strategy is studied for networked stochastic systems, where the output and input data are transmitted through multiple independent fading channels. The traditional P-type learning control scheme is revised according to the specific fading positions, where the constant learning gain is replaced by a variable one to suppress the effect of various uncertainties. Strong convergence of the proposed scheme is established under random fading phenomena and system noise. The input error is shown convergent to zero as the cycle number increases. Two numerical examples demonstrate the applications of the proposed scheme. [ABSTRACT FROM AUTHOR]

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Dominance robustness (DR) has been proposed for assessing the ability of the Pareto-optimal solutions to remain to be nondominated when the decision variables are subject to noise. There are two main challenges in search for dominance robust optimal solutions in dominance robust multiobjective optimization (MOP), namely, accurate estimation of the DR measure and a good balance between convergence and DR in the presence of uncertainty. In this article, a novel robust MOP evolutionary algorithm based on decision variable assortment (DVA) is proposed to tackle these challenges. To be specific, an indicator, termed as dominance robust indicator, is proposed to measure the DR based on the dominance level and dominance relationship of the sampled points. Then, the decision variables are divided into low DR-related variables and high DR-related variables based on the DVA strategy. Finally, low and high DR related variables are optimized separately to obtain the dominance robust optimal solutions. In addition, performance indicators to quantify the performance of dominance robust optimal solution set obtained by robust MOP algorithm are proposed. Experimental results have demonstrated that the proposed algorithm is competitive in search for dominance robust optimal solutions. [ABSTRACT FROM AUTHOR]

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms. [ABSTRACT FROM AUTHOR]

In this article, two Adams–Bashforth-type integration-enhanced discrete-time zeroing neural dynamic (ADTIZD) models are proposed to solve the time-varying complex Sylvester equation (TVCSE) problem in the first time. In ADTIZD models, Adams–Bashforth discrete formulas as novel discrete formulas are used, giving our ADTIZD models higher accuracy [truncation error being $O(\tau ^{5})$ ] but less time and space complexity than the ordinary multi-instant models. Enhanced by the integration part, the ADTIZD models can resist large additive noises, where even constant noises cannot decrease their precision. All convergence and robustness performance conclusions about our ADTIZD models are supported by rigorous theoretical proofs and numerical experiments. More comparisons between ADTIZD models and other discrete-time zeroing neural network models are shown in these experiments too. The efficacy of ADTIZD models is finally been validated in the simulation of adopting them in controlling a robotic manipulator. [ABSTRACT FROM AUTHOR]

Secure state estimation (SSE) is a problem to defense false-data injection attacks. This study designs an online distributed SSE of heterogeneous multiagent systems under homologous attack. A triple-loop observer is proposed to estimate the state and attack signal simultaneously. The inner loop keeps the estimations of the attack signal the same using average consensus. The middle loop adjusts the estimations via residual information. The outer loop runs when system measurements change. A sufficient condition that estimations asymptotically converge to the real value is obtained and proved. Finally, the proposed observer has been tested on the global positioning system. [ABSTRACT FROM AUTHOR]

Fixed-time stability (FXTS) and fixed-time control (FXTC) of dynamic systems are reconsidered in this article based on special functions from the view of improving the estimate accuracy of settling time (ST) and reducing the chattering caused by the sign function. First, by means of the idea of contradiction and variable transformations, some generic FXTS criteria are established and some upper bounds of ST are directly calculated and expressed by several special functions. It is further proved that these estimates are the most accurate compared with the existing results. Besides, to suppress the chattering caused by the sign function, some saturation functions are constructed to replace the sign function and the FXTS of the new system obtained by replacing is ensured by rigorous theoretical analysis. As applications, the problem of stabilization for chaotic systems in fixed or preassigned time is explored. Especially, an innovative saturation controller is developed to realize preassigned-time stabilization, where the convergence time is prescribed in advance according to actual requirement and the control gains are finite, the existing control methods with time-varying infinite gains are essentially improved. Lastly, three numerical examples are provided to verify the improved estimates of ST and the chattering reduction. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

This article addresses the fixed-time average consensus problem of nonlinear multiagent systems (MASs) subject to input delay, external disturbances, and switching topologies. Different from the finite-time convergence, the convergence time of the fixed-time convergence is independent of initial conditions. Then, an event-based control strategy is presented to reach the fixed-time average consensus under switching topologies and intermittent communication. Because the nonlinear dynamics, external disturbances, switching topologies, and triggering condition for intermittent communication are considered, the fixed-time consensus problem is more challenging under the event-based control than under the continuous-time control. Besides, a new measurement error is designed based on the hyperbolic tangent function to avoid Zeno behavior. Furthermore, an improved triggering function is designed to avoid continuous monitoring. Hence, resource consumption is reduced significantly. Finally, the effectiveness of the algorithms is validated by three simulation examples. [ABSTRACT FROM AUTHOR]

Complex-valued neural network is a kind of learning model which can deal with problems in complex domain. Fully complex extreme learning machine (CELM) is a much faster training algorithm than the complex backpropagation (CBP) scheme. However, it is at the cost of using more hidden nodes to obtain the comparable performance. An upper-layer-solution-aware algorithm has been proposed for training single-hidden layer feedforward neural networks, which performs much better than its counterparts, pseudo-inverse learning (PIL)/extreme learning machine and gradient decent-based backpropagation neural networks. Consequently, there exist two challenges that need to be dealt with: 1) How to combine the advantages of CBP and CELM to develop a novel complex learning algorithm? and 2) What is the convergent behavior of the presented algorithm? In this article, an input weights dependent complex-valued (IWDCV) learning algorithm based on Wirtinger calculus has been proposed, which effectively solves the nonanalytic problem of the common activation functions during training neural networks. In addition, the monotonicity of the error function and the deterministic convergence of the proposed model have been strictly proved, which theoretically guarantee the efficiency and effectiveness of the given model, IWDCV. Finally, for real and complex-valued problems, a variety of simulations have been done to demonstrate the comparable performance of the proposed algorithm which support the theoretical observations as well. [ABSTRACT FROM AUTHOR]

The extended state observer (ESO) used to estimate the unknown model for nonlinear systems has been widely applied in model-free control. In the ESO, three factors: 1) nonderivative structure; 2) insufficient usage of innovation; and 3) no compensation of the unknown character of a nonlinear function, causing low type and low accuracy of observation are identified. The convergence problem of the ESO is also raised. A simple linear compensation function observer (CFO) is proposed. The CFO adopts the derivative form overcoming the structure problem of the ESO, fully uses the available innovation, and then introduces a compensator to replace the unknown function. The filtering compensator counteracts the effect of the time-varying nonlinear unknown model to make the error equation behave with desired poles. The convergence of the CFO is theoretically proved. The CFO is the Type-III system, whereas the ESO is a Type-I system; therefore, the CFO has a qualitative leap over the ESO in accuracy improvement of observation. The CFO can observe nonlinear functions, including lumped disturbances, uncertainties, and unmodeled parts for nonlinear systems. The CFO decouples the multi-input and multioutput (MIMO) systems. Five unknown typical nonlinear functions are tested and demonstrates that the CFO qualitatively prevails over the ESO. The MIMO chaotic attitude system of a small-scale unmanned aerial vehicle (UAV) helicopter is conducted with results that CFO performance of function observation is highly improved over that of ESO about 29 times. [ABSTRACT FROM AUTHOR]

This article addresses the problem of synchronization of impulsive networks with switching topologies. A new synchronization framework is established with an emphasis on settling time estimation. The impulsive networks consist of physical nodes and cyber modules. For physical nodes, states are changed impulsively at discrete time instants due to some switching phenomena or unexpected sudden noises. For cyber modules, two cases of switching scenarios are considered for information exchange patterns during specific time intervals. In the first case, cyber modules lose all the communication links with others, resulting in disconnected topologies. Then, a distributed controller is proposed for nodes without intrinsic nonlinear dynamics. A distinguished feature of this controller is its capability to estimate a bound for settling time, beyond which the synchronization with respect to a virtual target is guaranteed. In the second case, cyber modules lose some communication links but build other new ones with the help of a smart communication center to form connected topologies. A distributed controller is further designed for nodes in the presence of intrinsic nonlinear dynamics. Accordingly, a sufficient condition is derived to achieve synchronization with an estimated settling time bound. For both cases, the estimated bounds are able to reveal the relationship between the impulsive strength and the synchronization performance. Finally, numerical examples including a case study on a modified IEEE 34 bus test feeder are provided to demonstrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Previous research on finite-time control focuses on forcing a system state (vector) to converge within a certain time moment, regardless of how each state element converges. In the present work, we introduce a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability (TSS), where at the same time, all the system state elements converge to the origin, and fixed-TSS, where the upper bound of the synchronized settling time is invariant with any initial state. Accordingly, sufficient conditions for (fixed-) TSS are presented. On the basis of these formulations of the time-synchronized convergence property, the classical sign function, and also a norm-normalized sign function, are first revisited. Then in terms of this notion of TSS, we investigate their differences with applications in control system design for first-order systems (to illustrate the key concepts and outcomes), paying special attention to their convergence performance. It is found that while both these sign functions contribute to system stability, nevertheless an important result can be drawn that norm-normalized sign functions help a system to additionally achieve TSS. Furthermore, we propose a fixed-time-synchronized sliding-mode controller for second-order systems; and we also consider the important related matters of singularity avoidance there. Finally, numerical simulations are conducted to present the (fixed-) time-synchronized features attained; and further explorations of the merits of the proposed (fixed-) TSS are described. [ABSTRACT FROM AUTHOR]

This article presents a novel technique for terminal-time synchronization of multivehicle systems. Taking sampled-data communications into account, the terminal-time synchronization problem of multivehicle systems is formulated as three demands. An estimation of terminal time is introduced for each vehicle, and a cooperative algorithm is designed based on motion planning to synchronize all estimated terminal times by using only local sampled-data information. The proposed algorithm not only can ensure the consensus of estimated terminal times at appointed time, but also can make the estimates finally be equal to the actual terminal times. To avoid Zeno behavior, the explicit expression of the norm of the consensus error is formulated, based on which the sampling interval sequence is modified to realize appointed-time approximate consensus of the actual terminal times. Local controller is also designed for each vehicle to ensure the fixed-time convergence of the relative velocity normal to the line of sight, and thus the singularity of control input at terminal time instant is successfully avoided. Experiments are performed to verify the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

In policy evaluation of reinforcement learning tasks, the temporal difference (TD) learning with value function approximation has been widely studied. However, feature representation has a decisive influence on both accuracy of value function approximation and convergence rate. Therefore, it is important to develop the feature selection theory and methods that can efficiently prevent overfitting and improve estimation accuracy in TD learning algorithms. In this article, we propose an online sparse TD learning algorithm for policy evaluation by using $\ell _{1}$ -regualrization for feature selection. The per-step-time runtime computational complexity of the proposed algorithm is linear with respect to feature dimension. The loss function is defined as a nested optimization with $\ell _{1}$ -regularization penalty, and the solver minimizes two suboptimization problems by running stochastic gradient descent and regularized dual averaging method, alternately. The convergence results for the fixed points are also established. The experiments on benchmarks with high-dimensional features show the abilities of learning and generalization of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

This article investigates a political party or an association social network where members share a common set of beliefs. In modeling it as a distributed iterative algorithm with network dynamics mimicking the interactions between people, the problem of interest becomes that of determining: 1) the conditions when convergence happens in finite time and 2) the corresponding steady-state opinion. For a traditional model, it is shown that finite-time convergence requires a complete topology and that by removing neighbors with duplicate opinions reduces in half the number of links. Finite-time convergence is proved for two novel models even when nodes contact two other nodes of close opinion. In a deterministic setting, the network connectivity influences the final consensus and changes the relative weight of each node on the final value. In the case of mobile robots, a similar communication constraint is present which makes the analysis of the social network so relevant in the domain of control systems as a guideline to save resources and obtain finite-time consensus. Through simulations, the main results regarding convergence are illustrated paying special attention to the rates at which consensus is achieved. [ABSTRACT FROM AUTHOR]

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs. [ABSTRACT FROM AUTHOR]

Optimal iterative learning control (OILC) has been recognized as an excellent model-based means for regulating batch process with abundant successful applications reported in the past decades but also received considerable criticisms for its poor robustness against model mismatch that is common for many industrial situations. Despite numerous attempts to address the issue, many of them are still not able to yield satisfactory control performance particularly in the presence of a possible combination of time-varying uncertainties and conservatively designed controllers, which may compromise the learning mechanism, hence rendering the robustness issue of OILC far from well explored. This article intends to investigate the aforementioned issue by proposing a new OILC method resting upon the minimization of a dynamic upper bound on tracking error which is distilled from better exploitation of the time variation of uncertainties. We also show that the problem can be formulated in the framework of convex–concave game that can be efficiently solved by a subgradient method with an excellent balance of optimality and computation time. Such a formulation enables us to gain: 1) guaranteed monotonic convergence on tracking error; 2) remarkably reduced conservatism on controller synthesis; and 3) controllable computation complexity. It is further shown that the proposed method is capable of handling nonlinearity, for example Volterra system, a classic representation of nonlinear process. The efficacy of the method is verified by numerical experiments on a continuous stirred tank reactor model. [ABSTRACT FROM AUTHOR]

This article presents and practically validates an identifier-critic-based approximate dynamic programming (ADP) method to online address the optimal tracking control problem for nonlinear continuous-time unknown systems. The imposed assumption on precisely known system dynamics is obviated via a neural network (NN) identifier. A static control is first adopted to retain the steady-state tracking response, while an optimal control derived via the ADP method is proposed to regulate the tracking error by minimizing a cost function. A critic NN is then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. The learning of the identifier NN and critic NN is performed online simultaneously by tailoring a novel adaptation method, which can guarantee the convergence of the estimated NN weights. Consequently, the critic NN can be used to construct the optimal control policy directly, such that the actor NN used in the previous ADP schemes is avoided. Simulations are performed to verify the suggested control, and experiments on a helicopter plant are carried out to show its feasibility and improved control response. [ABSTRACT FROM AUTHOR]

Currently, some works on studying complete synchronization of dynamical systems are usually restricted to its two special cases: 1) power-rate synchronization and 2) exponential synchronization. Therefore, how to give a generalization of these types of complete synchronization by the mathematical expression is an open question that needs to be urgently solved. To begin with, this article proposes multimode function synchronization by the mathematical expression for the first time, which is a generalization of exponential synchronization, power-rate synchronization, logarithmical synchronization, and so on. Moreover, two adaptive controllers are designed to achieve robust multimode function synchronization of memristive neural networks (MNNs) with mismatched parameters and uncertain parameters. Each adaptive controller includes function $r(t)$ and update gain $\sigma $. By choosing different types of $r(t)$ , multiple types of complete synchronization, including power-rate synchronization and exponential synchronization can be obtained. And update gain $\sigma $ can be used to adjust the speed of synchronization. Therefore, our results enlarge and strengthen the existing results. Two examples are put forward to verify the validity of our results. [ABSTRACT FROM AUTHOR]

This article proposes a global adaptive neural network tracking control method for uncertain strict-feedback nonlinear system with output constraint and dead zone to achieve predefined-time convergence of the tracking error to predefined accuracy. First, an integral-type Barrier Lyapunov function (BLF) is constructed to handle output constraint. Next, radial basis function neural network (RBFNN) control and robust control are used to tackle unknown nonlinear function. The continuous switching function is designed to switch RBFNN control to robust control when the arguments of the unknown function exceed the active region of neural network. Utilizing the property of radial basis function, we derive the upper bound of the term containing the unknown nonlinear function and design adaptive laws to determine the derived upper bound and robust control gain. Then, the predefined time virtual control inputs are obtained and their derivatives are estimated by finite time differentiator. Finally, we use the dead zone inverse technique to obtain the actual control input. Stability analysis shows the presented control scheme achieves global convergence of the errors to predefined accuracy within predefined time. The simulation results verify the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of scaled tracking consensus for discrete-time second-order multiagent systems under random packet dropouts, where the cases with a static leader and a dynamic leader are considered, respectively. The scaled tracking consensus means that all agents reach a consensus value determined by the leader but with different scales, and the phenomenon of packet dropout on each communication link is described as a Bernoulli variable independent of other communication links. By virtue of random environment-based scaled consensus algorithms, it is shown how to reconstruct the original system into augmented error systems with random coefficient matrices. With the kind assistance of substochastic matrix and super-stochastic matrix, sufficient conditions for the cases with a static leader and a dynamic leader are derived, respectively. Moreover, computer simulations are performed to demonstrate the dynamics of network agents under random packet dropouts. [ABSTRACT FROM AUTHOR]

In this article, the ultrafast tracking control for high-order discrete-time multiagent networks is investigated based on the predictive ability of agents. First, in view of the evolution of the original network dynamics, a distributed multistep prediction algorithm is established. Further, a control strategy containing predictive information is presented to achieve the ultrafast tracking control. Second, the problem of ultrafast tracking control with an $H_{\infty }$ performance specification is dealt with. The obtained result indicates that the robustness of the whole multiagent network can be converted into the robustness of multiple separable subsystems. Finally, the optimal ultrafast static tracking control design is provided for the single-integrator network with sampled dynamics. Two simulation cases are carried out to verify the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

A social cost minimization problem is addressed in this article. In the considered problem, a network of agents work collaboratively to minimize the social cost function, which is defined as the sum of the agents’ local objective functions. The engaged agents are supposed to be equipped with an undirected and connected communication graph. Different from most of the existing works, the social cost function in the considered problem is allowed to be nonconvex and possibly admits local extrema. To avoid local extrema and achieve the global minimization of the social cost function, an extremum-seeking-based approach is proposed by introducing a dynamic average consensus protocol to the sinusoidal-dither-signal-based extremum seeking scheme. The dynamic average consensus protocol is leveraged in the proposed extremum-seeker for information sharing and the sinusoidal probing signal is utilized for information extraction. For the avoidance of local extrema, the amplitude of the dither signal is designed to be adaptive. Through Lyapunov stability analysis, it is shown that the proposed method enables the decision variable to converge to a neighborhood of the global minimum point if the conditions on the network connectivity, the existence of unique global minimum and achievability of the global minimum are satisfied. The theoretical result is verified via simulating a numerical example. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of global finite-time output stabilization for a class of second-order nonlinear systems with both uncertain nonlinear dynamics and unknown external disturbance. Specifically, at the first step, without considering the external disturbance, a global finite-time state feedback controller is proposed to dominate uncertain nonlinear dynamics of the second-order system. To address the more challenging case where only the system output is available, a novel design idea of the nonseparation principle is employed. By treating the unknown external disturbance as a generalized state, a finite-time convergent extended state observer is constructed to estimate the unmeasured state and the unknown external disturbance. Based on this observer, an output-based composite controller with finite-time convergence is developed. The global uniform finite-time stability of the overall closed-loop system is proven based on the Lyapunov method. Simulation results of the inverted pendulum system demonstrate the superiority of the proposed control method in terms of both convergence performance and disturbance rejection performance. [ABSTRACT FROM AUTHOR]

Optimization is an important research field, especially in engineering, physical sciences, and economics. The main purpose of optimization is to maximize the profit and minimize the cost of production as well as the loss of the system. Evolutionary computation algorithms, such as the genetic algorithm and the particle swarm optimization (PSO) algorithm have been successfully employed in solving various optimization problems. Owing to its application potential and promising performance in discovering the optimal solution, the PSO algorithm has been recognized as a powerful optimization technique and attracted an ever-increasing interest in the evolutionary computation community. In this article, a novel $N$ -state Markovian jumping PSO (NS-MJPSO) algorithm is presented where the velocity updating equation is adjusted based on the state evolution governed by a Markov chain. The performance of the proposed NS-MJPSO algorithm is evaluated via some widely used mathematical benchmark functions. The experimental results demonstrate that the developed NS-MJPSO algorithm outperforms some currently popular PSO algorithms on the widely used benchmark functions. [ABSTRACT FROM AUTHOR]

This article studies the distributed composite optimization problem over relay-assisted networks (DCOP-RNs). By combining the local primal–dual updates with a data fusion strategy, an effective distributed algorithm is developed to solve the DCOP-RN. Compared with the existing linearized alternating direction method of multipliers (ADMMs), this article provides a novel interpretation of the proposed algorithm. More specifically, it is shown that the proposed algorithm can be interpreted as a simplified proximal augmented Lagrangian method. Within this framework, a simplified convergence analysis of the algorithm is conducted, based on which the convergence to an optimal solution to the DCOP-RN is proved. Further, taking into account the limited bandwidth in real networks, this article proposes a quantized distributed algorithm to solve the DCOP-RN. Especially, a relationship between the quantization resolution and the convergence accuracy of the algorithm is established. Finally, simulation examples verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we concentrate on dealing with the distributed optimization problem over a directed network, where each unit possesses its own convex cost function and the principal target is to minimize a global cost function (formulated by the average of all local cost functions) while obeying the network connectivity structure. Most of the existing methods, such as push-sum strategy, have eliminated the unbalancedness induced by the directed network via utilizing column-stochastic weights, which may be infeasible if the distributed implementation requires each unit to gain access to (at least) its out-degree information. In contrast, to be suitable for the directed networks with row-stochastic weights, we propose a new directed distributed Nesterov-like gradient tracking algorithm, named as D-DNGT, that incorporates the gradient tracking into the distributed Nesterov method with momentum terms and employs nonuniform step-sizes. D-DNGT extends a number of outstanding consensus algorithms over strongly connected directed networks. The implementation of D-DNGT is straightforward if each unit locally chooses a suitable step-size and privately regulates the weights on information that acquires from in-neighbors. If the largest step-size and the maximum momentum coefficient are positive and small sufficiently, we can prove that D-DNGT converges linearly to the optimal solution provided that the cost functions are smooth and strongly convex. We provide numerical experiments to confirm the findings in this article and contrast D-DNGT with recently proposed distributed optimization approaches. [ABSTRACT FROM AUTHOR]

Only partial system knowledge for the generalized robotic dynamics with input saturation, i.e., the regression matrix for the specific robot, is required to design the proposed adaptive finite-time saturated tracking control (AFTSTC). It contains a nonlinear auxiliary tracking error, which can shape the system frequency response. As the operating point is in the neighborhood of the zero auxiliary tracking error, nonlinear filtering gains can be increased to accelerate its tracking ability. Moreover, the traditional skew-symmetric matrix’s condition for the time derivative of inertia matrix and the Coriolis and centrifugal force matrix is not necessarily required such that the uncertainties and the finite-time convergence are reduced. The computational complexity as compared with the fuzzy neural network adaptive control is also addressed. The stability of the closed-loop system is verified by the Lyapunov stability theory. Finally, two practical robotic examples are given to validate the effectiveness and robustness of the proposed control. [ABSTRACT FROM AUTHOR]