Search

This paper concentrates on proposing a novel finite-time tracking control algorithm for a kind of nonlinear systems with input quantization and unknown control directions. The nonlinear functions in the system are approximated by the means of strong approximation capability of the fuzzy logic systems. Firstly, the nonlinear system with unknown control directions is transformed into an equivalent system with known control gains by coordinate transformation. Secondly, the unknown system states are estimated by a designed fuzzy state observer, and the disturbance observer is constructed to track the external disturbances. The command filtering method is proposed to approach the problem of "explosion of complexity" existed in the conventional backstepping design process. In this system, the difficulties caused by unknown control directions are solved via the Nussbaum gain approach. Finally, based on the fuzzy state observer, the controller of the original system is obtained via using the transformed system by the backstepping method. The boundedness of all signals and the convergence of tracking and observer errors at the origin are ensured for the closed-loop system, and demonstrated by the simulation result in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the leader-follower finite-time consensus problem for multiagent systems with nonlinear dynamics via intermittent protocol. The topological structure of the followers is undirected or balanced digraph. Different from most existing works concerning nonlinear dynamics (satisfies Lipschitz continuity), the nonlinear dynamics of each agent satisfies Hölder continuity in this paper. In light of the finite-time control technique, the intermittent control protocol is designed to reach accurate leader-follower finite-time consensus. It is justified that the leader-follower finite-time consensus can be realized if the length of communication is greater than a critical value by using limit theory. Finally, two numerical examples are exhibited to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback based periodic event-triggered control problem is considered for a class of nonminimum-phase nonlinear systems via dynamic event-triggering mechanism. When only the sampled-data output is known, a new periodic event-triggered control method is proposed via output feedback and the control input updates based on a discrete-time dynamic event-triggering condition. Despite the unstable zero dynamics, the proposed control method can asymptotically stabilize the hybrid control systems by closing the loop only when it is necessary. In contrast to the continuous-time static one, the proposed dynamic triggering condition has several advantages including the easier digital implementation and the larger average inter-event time interval. The delicate analysis gives the explicit expression of the maximum allowable sampling period, and the global asymptotic stability can be achieved for the hybrid control systems. Finally, the effectiveness of the proposed periodic event-triggered control method is verified by a numerical simulation. [ABSTRACT FROM AUTHOR]

The problem of generalized dissipative state estimation for discrete-time nonhomogeneous semi-Markov jump nonlinear systems is concerned in this paper. In this paper, we consider the semi-Markov renewal chain is nonhomogeneous and the states of the system are inaccessible. The aim of this paper is to propose the estimator-designed method to ensure that the system is σ -mean-square stable and satisfy extended dissipative performance. By using the semi-Markov kernel method and polytopic approach, and constructing a new type of Lyapunov function, which not only depends on the sojourn-time but also on the stochastic switching rules, the state estimator gains can be obtained. At last, a numerical example is adopted to verify the superiority of the presented control strategy. [ABSTRACT FROM AUTHOR]

In this paper, the observer based neural adaptive finite-time containment control strategy for non-strict feedback nonlinear multi-agent systems is studied. The finite-time command filter is used to overcome the explosion of complexity problem and the established fractional power based error compensation signal is applied to compensate the filtering error caused by the filter. The distributed finite-time command filtered backstepping control method combines with the neural adaptive control technology and state observer is given, which ensures the containment control errors reach to the desired neighborhood of the origin in finite-time in the presence of uncertain dynamics and unmeasurable states in the system. The given numerical simulations show the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the secure consensus tracking problem for continuous-time nonlinear multiagent systems with sensor attacks. By designing a secure data selector, the unattacked output data is extracted from a group of output measurements under sparse sensor attacks. Then, by virtue of the obtained data and neural networks, a state observer is constructed to estimate the unavailable system states, where the convex combination theory is introduced to reduce the difficulty of solving observation gains. To utilize the limited communication resources reasonably, a novel saturated threshold event-triggered control strategy is proposed to reduce control updates, and then each update is encoded into a binary signal (0 or 1) to further reduce the occupation of communication bandwidth. The designed control scheme ensures that all closed-loop signals are semi-globally uniformly ultimately bounded, and its effectiveness is verified via a simulation of attitude control of unmanned aerial vehicles. [ABSTRACT FROM AUTHOR]

This paper focuses on an adaptive fuzzy fixed-time control problem for stochastic nonstrict nonlinear systems with unknown dead-zones by using dynamic surface control (DSC) technology. Fuzzy logic systems (FLSs) and DSC technology are used to approximate nonlinear functions and reduce the computational complexity, respectively. At the same time, the influence of the dead-zone disturbance is offset by transforming the dead-zone model into the nonlinear model that can be approximated by the FLSs. Then, based on the fixed-time stability theory, an adaptive fuzzy fixed-time tracking control strategy is proposed, which can ensure semi-global practical fixed-time stability of the system and the tracking error converging to a small neighborhood near the origin. Finally, two simulation examples are given to prove the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the precise containment control problem for nonlinear multi-agent systems (MAS) subject to non-vanishing uncertainties and unknown non-identical control directions under directed communication topology. Due to the existence of the inherent non-vanishing/non-parametric uncertainties and unknown control directions, the precise (zero-error) containment control synthesis becomes nontrivial. The underlying problem becomes even complicated if the convergence rate is required to be pre-specified. This work aims at circumventing the aforementioned difficulties to derive a precise containment control solution. The salient features behind the derived algorithms are: i) the non-vanishing uncertainties are completely rejected; ii) the containment error is regulated to zero at prescribed convergence rate, in spite of the non-vanishing uncertainties and unknown non-identical control directions; and iii) the full-state containment rather than output containment is achieved. A simulation example is given to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the observer-based consensus control for high-order nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. When the DoS attacks appear, the communication channels are destroyed, and the blocked information may ruin the consensus of MASs. A switched state observer is designed for the followers to observe the leader's state whether the DoS attacks occur or not. Then, a dynamic event-triggered condition is proposed to reduce the consumption of communication resources. Moreover, an observer-based and dynamic event-triggered controller is formulated to achieve leader-following consensus through the back-stepping method. Additionally, the boundedness of all closed-loop signals is obtained based on the Lyapunov stability theory. Finally, the simulation results demonstrate the effectiveness of the presented control strategy under DoS attacks. [ABSTRACT FROM AUTHOR]

The reinforcement learning-based prescribed performance optimal tracking control problem is considered for a class of strict-feedback nonlinear systems in this paper. The unknown nonlinearities and cost function are approximated by radial-basis-function (RBF) neural network (NN). The overall controller consists of an adaptive controller and an optimal compensation term. Firstly, the adaptive controller is designed by backstepping control method. Subsequently, the optimal compensation term is derived via policy iteration by minimizing cost function. In addition, depending on the prescribed performance control, the tracking error can be limited in the prescribed area. Therefore, the whole control scheme can effectively guarantee that the tracking error converges to a bound with prescribed performance while the cost function is minimized. The stability analysis shows that all signals in the closed-loop system are bounded. Finally, the effectiveness and advantages of the designed control strategy are illustrated by the simulation examples. [ABSTRACT FROM AUTHOR]

This paper deals with adaptive neural networks (NNs) output-feedback tracking control problem for a general class of switched nonlinear time-delay systems with actuator saturation. To estimate unmeasurable states, a constructive delay-independent switched-observer-based adaptive NNs control approach for solving the problem is provided by using the average dwell time (ADT) method and the backstepping technique. Design obstacles stemmed from unknown time delays and actuator saturation and unknown nonlinear functions are overcome by using appropriate multiple Lyapunov–Krasovskii functionals method, the Nussbaum gain technique, and neural network approximations, respectively. The proposed control strategy guarantees that i) all the closed-loop signals for the switched system are bounded in the semi-global sense under a class of switching signals with ADT, attaining semi-global uniformly ultimately boundedness (SGUUB); and, ii) the output tracking error is driven towards, and kept within, a small neighbourhood around the origin. Simulation results verify the effectiveness of the proposed control strategy on two numerical examples, including a practical switched continuous stirred tank reactor (CSTR) system. [ABSTRACT FROM AUTHOR]

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the issues of non-fragile event-triggered consensus problem for nonlinear multiagent systems (MASs) with external disturbance subjected to randomly occurring packet losses and periodic Denial of Service (DoS) attacks. Under connected communication topology, each agent exchanges information with its neighbors. In the presence of packet losses and DoS attacks, an event-triggered mechanism is designed to decide when to communicate the current sampled-data. Randomness is solved by using Bernoulli distribution in a stochastic way and the external disturbance is handled by using H ∞ performance. A sufficient condition is derived in terms of linear matrix inequalities (LMIs) by introducing time-varying Lyapunov–Krasovskii Functional (LKF), ensuring mean square consensus for the resulting closed-loop systems. Finally, to show the effectiveness and applicability of proposed control scheme, two numerical simulations are presented. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to describe a novel implementation of a multispatial method, multitime-scheme subdomain differential algebraic equation (DAE) framework allowing a mix of different space discretization methods and different time schemes by a robust generalized single step single solve (GS4) family of linear multistep (LMS) algorithms on a single body analysis for the first-order nonlinear transient systems. Design/methodology/approach: This proposed method allows the coupling of different numerical methods, such as the finite element method and particle methods, and different implicit and/or explicit algorithms in each subdomain into a single analysis with the GS4 framework. The DAE, which constrains both space and time in multi-subdomain analysis, combined with the GS4 framework ensures the second-order time accuracy in all primary variables and Lagrange multiplier. With the appropriate GS4 parameters, the algorithmic temperature rate variable shift can be matched for all time steps using the DAE. The proposed method is used to solve various combinations of spatial methods and time schemes between subdomains in a single analysis of nonlinear first-order system problems. Findings: The proposed method is capable of coupling different spatial methods for multiple subdomains and different implicit/explicit time integration schemes in the GS4 framework while sustaining second-order time accuracy. Originality/value: Traditional approaches do not permit such robust and flexible coupling features. The proposed framework encompasses most of the LMS methods that are second-order time accurate and unconditionally stable. [ABSTRACT FROM AUTHOR]

One of the drawbacks of the controllability theory for nonlinear systems is that most existing controllability criteria are not algebraically verifiable, which makes them difficult to apply especially if the system dimension is high. Thus, it is a significant task to seek algebraically verifiable controllability criteria for nonlinear systems. In this paper, we study controllability of discrete-time inhomogeneous bilinear systems. In the classical results on controllability of such systems, a necessary condition is that the linear part has to be controllable. However, we will show that this condition is in fact not necessary for controllability. Specifically, we first define the spectrum for discrete-time inhomogeneous bilinear systems and reveal that the spectrum is a fundamental property which is very useful in investigating the controllability problems. We then present controllability criteria for the systems with real spectrum, which are algebraically verifiable. Furthermore, we also provide algorithms for the controllable systems to compute the exact or approximated control inputs to achieve the transition between any given pair of states. The presented controllability criteria and algorithms work for the systems in any finite dimension and are easy to implement. More importantly, through our controllability criteria, we reveal that controllability of the linear part is not necessary for discrete-time inhomogeneous bilinear systems to be controllable. Examples are given to illustrate the presented algebraic controllability criteria. [ABSTRACT FROM AUTHOR]

The core objective of this paper is to investigate the problem of robust nonlinear observer-based controller design for one-sided Lipschitz (OLS) switched systems. This work considers nonlinear switched systems with norm-bounded uncertainties, time-varying delays, and external disturbances. By selecting appropriate Lyapunov-Krasovskii functions and applying the OSL condition together with the quadratic inner boundedness property, we drive certain necessary and sufficient conditions for the observer-based control of the underlying system that assure the exponential convergence of the system states, the observer states, and the error states to zero, in respect of linear matrix inequalities via average dwell-time approach. The devised scheme offers necessary robustness against L 2 -norm bounded perturbations. In the end, the proposed scheme has been validated a suitable practical example. [ABSTRACT FROM AUTHOR]

The practical finite-time control problem of uncertain nonlinear systems is investigated in this paper. To address the uncertain nonlinearities of the system, neural networks are introduced to approximate the lumped nonlinearities containing the system unknown functions. On the other hand, to alleviate the signal transmission pressure of the system, an improved event-triggered mechanism is presented to reduce the controller update frequency without degrading the control performance of the system. By using practical finite-time stability, it is obtained that the system tracking errors are practical finite-time stable without Zeno behavior. Finally, the effectiveness of the proposed method is verified by the simulation results of its application to a microwave plasma chemical vapor deposition (MPCVD) reactor system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the finite-time scaled consensus tracking of a class of high-order nonlinear multiagent systems(MASs)who owns unstable modes in its Jacobian linearized system. The presence of unstable linearization makes the high-order MASs in question essentially different from those in the existing works. Under a directed interaction topology, to overcome the difficulties caused by the asymmetry property of Laplacian matrix, the finite-time scaled consensus control scheme is developed by the modified addition of a power integrator method. Based on finite-time Lyapunov stability theorem and algebra graph theory, for high-order MASs with unstable linearization even in the presence of non-lipschitz nonlinear dynamic, all system states are bounded and the output tracking errors are finite-time uniformly ultimately bounded(FUUB). Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops new practical stability criteria for continuous-time stochastic nonlinear system with uncertainties and external disturbances. Two cases of the system are considered: the system with state-dependent disturbance and the system with state-independent disturbance. Based on the event-triggered mechanism and Lyapunov function, we establish the input-to-state practical exponential stability in mean square for each case of the system. The obtained results improve some previous works in the literature. Finally, several examples are given to show the effectiveness and practicability of the main results. [ABSTRACT FROM AUTHOR]

This paper considers a trilayer Stackelberg game problem for nonlinear system with three players. A novel performance function is defined for each player, which depends on the coupling relationships with the other two players. The coupled Hamilton–Jacobi–Bellman (HJB) equations are built from the performance functions, and the optimal control polices of three players are obtained based on the Bellman's principle of optimality. Because of the nonlinearity and coupling characteristics, a policy iteration (PI) algorithm with a three-layer decision-making framework is developed to online learn the coupled HJB equations. In order to implement the algorithm, we construct a critic-action neural network (NN) structure and design a NN approximation-based iteration algorithm. Finally, a simulation example is presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates H ∞ leader-follower consensus problems of nonlinear multi-agent systems via event-triggered control. To significantly reduce the communication burdens, a distributed estimator-based event-triggered communication protocol is proposed. By using Lyapunov stability theory, matrix theory and algebraic graph theory, we derive some sufficient conditions to guarantee the leader-follower consensus with desired H ∞ performance. Distributed triggering functions are designed for three cases: fixed topologies, switching topologies with connected sub-topologies and frequently connected switching topologies. Furthermore, we prove that the Zeno-behavior can be excluded for three cases, respectively. Finally, simulations are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy output feedback control scheme is proposed for a class of unknown nonlinear systems with sensor attacks. The fuzzy logic systems are employed to approximate the uncertain nonlinearities, and the backstepping technique is implemented to construct controllers. The unknown output feedback coefficient is handled by using a Nussbaum function in the first step of backstepping design, eventually developing an adaptive controller to accommodate sensor attacks. Compared to the current control schemes for nonlinear systems under sensor attacks, the benefit of the proposed adaptive controller is that it can apply to nonlinear systems with both uncertainty and unmeasurable states. Finally, two examples validate the efficacy of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback adaptive control problem of uncertain nonlinear system with event-sampled states is studied. Firstly, a novel intermittent-state observer is designed to estimate the unmeasurable states. Secondly, the nature of event-triggered makes the state signals discontinuous, rendering the traditional backstepping technique inapplicable as the derivatives of virtual control signals do not exist. To overcome this non-trivial obstacle, we consider the case without state-triggering in the previous n − 1 steps of Lyapunov stability analysis, and reconstruct the actual controller by utilizing the triggered states signals in the last step. It can be demonstrated that all signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) under the derived event-triggered laws and the system performance can be improved by tuning design parameters properly. Simulation examples are shown to validate the efficacy of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In the present paper, we developed the functional matrix of integration via Bernoulli wavelets and generated a competent numerical scheme to solve the nonlinear system of singular differential equations which is Lane Emden form by Bernoulli wavelets collocation technique (BWCT) with different physical conditions. The system of nonlinear singular models is not smooth to operate as they are singular and nonlinear. This approach obtains the solution for this system by transforming it into a-nonlinear system of algebraic equations by expanding through Bernoulli wavelets with unknown coefficients. These unknown coefficients are calculated using the collocation scheme. The consistency and proficiency of the developed approach are demonstrated via graphs and tables. Attained results confirm that the newly implemented approach is more effective and accurate than other techniques which are available in the literature. All computations have been made using Mathematica software. The convergence of this method is explained in terms of theorems. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive event-triggered (AET) control, efficient model predictive control (EMPC) and output feedback control co-design approach for uncertain nonlinear systems over networks with bounded disturbance and data loss. The AET control involving a novel adaptive law is utilized to further reduce data transmission in networked control systems. Involving the technique of quadratic boundedness (QB), a class of output feedback predictive controllers based on the EMPC strategy are designed by minimizing several offline optimization problems and one online optimization problem. The approach in this paper, which transfers abundant online design work to offline, provides an offline determined augmented control invariant set for significantly reducing real-time computational load. Through the introduction of a novel matrix partition method moreover, the conventional online optimization problem of EMPC is transformed into a new form which is convenient to solve in this paper. A numerical example including some comparative experiments is proposed to clarify the availability of this approach. [ABSTRACT FROM AUTHOR]

In this paper, the containment control problem is investigated for a class of non-strict feedback nonlinear multi-agent systems with arbitrary initial states. The state observation disturbance, defined as the deviation between the observed and true values of the state, is taken into account in the addressed system. Fuzzy logic systems and adaptive techniques are accordingly introduced to handle the unknown nonlinear terms and unknown disturbances. Based on a transformation function and a new Lyapunov function, an improved fuzzy adaptive control protocol is developed, which ensures that the output tracking error of each follower converges to a predefined region within a predefined settling time and allows the initial states of the agents to be arbitrarily bounded. Moreover, the error (between the input and output of the filter inherent to the dynamic surface control) can be accurately compensated under the newly designed Lyapunov function. The simultaneous consideration of the asymmetric input saturation and unknown time-varying control gain coefficients in the model makes the results established in this paper more general. Finally, the effectiveness of the proposed control protocol is verified by two simulation experiments. • Agent's system is the more general non-strict feedback system. • The initial value of the agent's state can be arbitrary. • State observation disturbance is considered. • This paper employs adaptive control techniques. [ABSTRACT FROM AUTHOR]

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, a second-order-disturbance-observer-based distributed consensus control scheme is designed for a class of nonlinear multi-agent systems with input constraints. The second-order disturbance observer tracks the disturbance better than the common first-order disturbance observer. This paper provides the analysis of two kinds of disturbance observers and then compares the results from a simulation of the two types of observers. In the controller design process, a hyperbolic tangent function is used to limit output feedback in the control law. The overall closed-loop system reaches global stability with disturbance and the tracking errors exponentially converge without disturbance. The effectiveness of the proposed control law is illustrated by simulation results. • A novel disturbance observer is proposed. The estimation error is smaller. • The overall stability of the systems and the input constraints are realized. • Multi-agent systems converge exponentially with input constraints. [ABSTRACT FROM AUTHOR]

Due to the maturation of research on chaos and secure communication, the control technology of nonlinear systems, specifically chaos synchronization, has captured the attention of numerous researchers. Focusing on the issues of inflexibility in the design of chaotic synchronization controllers, the need for prior synchronization of the target system structure, and noise's disruptive impact on synchronization, this paper presents solutions that enhance the practical application of chaos. Firstly, the RBF neural controller is adjusted in this paper to bolster the control precision of the chaotic system and enhance its resilience to external disturbances. Secondly, this article presents an enhanced PSO optimization algorithm for the improved RBF neural controller to improve the optimization efficiency of the controller parameters. Finally, the simulation results of the Lorenz system validate the feasibility of the proposed synchronization control scheme. Additionally, the use of chaotic synchronization in image encryption demonstrates that synchronization accuracy can fulfill the requirements of image encryption application scenarios. • The structure of the RBF neural controller is improved to achieve better synchronization control performance, including synchronization accuracy and noise resistance. • The PSO algorithm is improved specifically for the intelligent chaotic controller studied in this article to enhance the efficiency of searching for RBF controller parameters. • Reduce the number of controllers used for synchronizing, improve the robustness of the synchronization system to noise, and a flexible and straightforward chaotic synchronization controller design. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive sliding mode control issue for switched nonlinear systems with matched and mismatched uncertainties is addressed, where the persistent dwell-time switching rule is introduced to describe the switching of parameters. Besides, considering the case that the upper bound of the matched uncertainty is unknown, the purpose of this paper is to utilize an adaptive control method to estimate its upper bound parameters. To begin with, a linear sliding surface is constructed, and then the reduced-order sliding mode dynamics can be obtained through a reduced-order method. Next, sufficient conditions can be derived based on the Lyapunov stability and the persistent dwell-time switching analysis techniques ensuring that the reduced-order sliding mode dynamics is globally uniformly exponentially stable. Moreover, a switched adaptive sliding mode control law is designed, which can not only ensure the reachability of the sliding surface but also estimate the upper bound parameters of the matched uncertainty. Finally, a numerical example and a circuit model are introduced to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive distributed control protocol is proposed for non-affine multi-agent system with nonlinear dead-zone input and state constraints under the condition of directed topology. In order to overcome the difficulties caused by non-affine terms in the system, the nonlinear dynamics system is transformed. Then, the neural network technology is introduced to approximate the unknown non-affine terms for the obtained system. State constraints and dead-zone input are common system problems. In order to solve these problems, the barrier Lyapunov function is introduced in this paper. According to the barrier Lyapunov function and backstepping method, an adaptive distributed controller is designed, so that state variables do not violate constraint bounds and the system is not affected by dead-zone input. By Lyapunov stability theory, it is proved that the signals of each follower are cooperative semi-global uniform ultimate boundedness (CSUUB), and the outputs of the followers track the output of the leader. Simulation example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time state bounding problem of homogeneous nonlinear positive systems with disturbance. Based on a technique used in positive systems, explicit conditions are established such that all solutions of homogeneous nonlinear positive systems with degree 0 < p < 1 converge to a ball in finite time. The approach used in this paper is different from the usual Lyapunov-Krasovskii functional method. We also extend the main result to the general nonlinear time-varying systems. Finally, two numerical examples are given to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

• This paper studies the generation of the stable limit cycle for the nonlinear sandwich systems with sandwiched dead-zone and input saturation nonlinearity which suffer from the unknown parameters. • To cope with complexity caused by the sandwiched dead-zone, a new description based on the property of the dead-zone nonlinearity is proposed. • To deal with the effect of the input saturation nonlinearity, the Gaussian error function is employed. • To solve the problem of ''explosion of complexity" in the recursive procedure of the backstepping approach, a finite-time differentiator is proposed. • The proposed controller guarantees the convergence of system trajectories to the desired limit cycle despite the occurrence of both saturation and dead-zone nonlinearities and existence of unknown parameters. This paper is concerned with the problem of generating stable limit cycles for a class of nonlinear sandwich systems with the sandwiched dead-zone nonlinearity. In this study, the considered sandwich systems are restricted to the potential problems of non-symmetric input saturation nonlinearity and unknown parameters. In this regard, based on the set stabilization approach and the shape of the desired limit cycle, an adaptive state feedback controller is constructed by using the backstepping technique in such a way that forces the system's output to oscillate with the wanted amplitude and frequency. Besides, to estimate the value of unknown parameters, the adaptive laws are extracted and the problem of the explosion of complexity in the traditional backstepping approach is solved via an effective differentiator. The Lyapunov stability analysis proves that all signals of the closed-loop system keep bounded. Finally, the simulation results of a practical example are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms. • This paper proposes a new hybridization Whale Optimization Algorithm and Flower Pollination Algorithm. • We solve system of nonlinear equations and unconstrained optimization problem. • The efficiency and effectiveness of our algorithm are provided. • Experimental results prove the superiority of our algorithm over the state-of-the-arts. [ABSTRACT FROM AUTHOR]

This paper discusses the distributed fixed-time containment control for networked nonlinear systems via the event/self-triggered approaches over directed graphs. A distributed event-triggered control protocol without continuous control updates is first proposed. In order to relieve the chattering effect, a modified distributed event-triggered control law is developed. To further overcome the drawback of continuous state monitoring and reduce the communication frequency between neighboring agents, a distributed chattering-free self-triggered control strategy is accordingly designed. A favorable aspect of our work is that the unnecessary resource utilizations of computation, communication as well as control updates can be saved while sustaining the desired control properties and excluding the Zeno behavior. Another distinct feature of this paper lies in that the containment control objective is realized in fixed time and the estimate of settling time can be prescribed without dependence on initial states of networked agents. Finally, some simulation results are provided to illustrate the effectiveness of the theoretical control schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the output feedback tracking control problem is investigated for polynomial nonlinear systems (PNSs) with measurement noises and mismatched disturbances. First, in order to suppress measurement noises, a polynomial observer is introduced to simultaneously estimate states and mismatched disturbances. Next, based on the idea of backstepping control, a novel output feedback controller is designed for PNSs to compensate mismatched disturbances. Command filters are employed to avoid the repeated derivatives of virtual control and measurement noises in the recursive controller design. Then, a sufficient condition in terms of the parameter-dependent linear matrix inequality (PDLMI) is derived to guarantee the boundedness of tracking errors and estimation errors. By utilizing the sum of squares (SOS) decomposition technique, the PDLMI is solved to obtain desired controller parameters. Finally, an example of dynamic point-the-bit rotary steerable drilling tool system is performed to demonstrate the effectiveness and feasibility of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper considers the stability of the random perturbation nonlinear delay system with intermittent stochastic noise. Under the interference of two different random noises, by using the Itô formula, the adequacy conditions for the stability of the system are given. At the same time, it is proved that when τ has an upper bound, the nonlinear delay system is almost surely exponentially stable and exponentially stable in p th moment. Furthermore, the correctness of the developed methods is illustrated by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI's) or linear matrix inequalities (LMI's). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered tracking control design for state-constrained switched nonstrict feedback nonlinear systems. With the help of a time-varying nonlinear shifting function (TVNSF) introduced into the switched nonlinear system, the proposed solution is seen as a unified tool regardless of whether the constraint conditions are state constraints, output constraint, or even no constraint. Also, by allowing the triggering error to vary with the switching signal in time, the negative effects of the mismatch between the individual controller and the subsystem on system performance are trumped. Moreover, by using constructed individual Lyapunov function that depends on the lower bound of the control gain function of individual subsystem, a novel switching signal satisfying the average dwell time (ADT) is provided to ensure the boundedness of all variables in the closed-loop system. Finally, the proposed theory is carried over into a mass-spring-damper system to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of asymptotic tracking control of nonlinear robotic systems with prescribed performance. The control strategy is developed based on a modified prescribed performance function (PPF) to guarantee the transient behavior, while the requirements on the accurate initial tracking error in the classical PPF can be remedied. The fuzzy logic system (FLS) is used to approximate the unknown dynamics. In the existing PPF based adaptive control schemes with FLSs, the tracking error does not achieve asymptotic convergence. To address this issue, a robust integral of the sign of the error (RISE) term is incorporated into the control design to reject the FLS approximation errors and external disturbances, such that the asymptotic convergence is achieved. Finally, numerical simulation and experimental results validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a fault detection and isolation (FDI) scheme for a class of uncertain nonlinear systems with unknown faults, in which fault isolation process and control reconfiguration are integrated via a supervisory switching strategy. A group of adaptive estimators is performed together with the switching process. The proposed FDI approach, namely dual-monitoring model-based approach, can exploit information both from backstepping procedure and estimators, by which a set of monitoring functions is constructed to detect the occurrence of fault and also identify the specific fault type. In particular, based on some principles, the fault isolation process can be accelerated under a novel interacted isolation scheme. It can be seen that the tracking error can be always guaranteed within a prescribed performance in the existence of system faults. [ABSTRACT FROM AUTHOR]

This paper studies the distributed output-feedback consensus tracking problem for nonlinear multi-agent systems (MASs) subject to dynamic output constraints and input saturation. Firstly, a neural-network (NN) based high gain observer is designed to provide estimation for unmeasured state of each agent. To address the dynamic output constraints problem, a unified barrier function is proposed to convert the constrained system into unconstrained one. Then, command filter-based backstepping is applied in design procedures to construct the distributed consensus tracking protocol and adaptive law. The auxiliary systems are constructed to generate additional error signals which are used to reduce the influence of input saturation. Thirdly, the boundedness of all signals in closed-loop MASs is proved based on Lyapunov stability theory. The consensus tracking error converges to an arbitrarily small neighborhood around the origin and the general dynamic output constraints are not violated under saturated input. Finally, The effectiveness of the proposed control protocol is verified using a simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of reliable mixed H 2 / H ∞ distributed state estimation for periodic nonlinear systems. A sensor network with time-varying topology is used to measure the system, where the time-varying condition is described by a period index dependent Markov chain. A distributed state estimator is designed based on the local and neighbors' innovation information of each node, while the non-fragile estimator is considered to improve the robustness of the estimator. An augmented estimation error system is derived, while the developed sufficient condition is carried out to ensure the stochastic stability and the mixed H 2 / H ∞ performance. Then, the expected estimator gains are solved on the basis of the achieved sufficient condition. Finally, the effectiveness of the proposed state estimation method is emphasized by a numerical example and the comparative experiments. [ABSTRACT FROM AUTHOR]

The paper is concerned with mean-square group consensus for second-order multi-agent systems with non-identical dynamics, where the agents in the same group have the identical dynamics, the agents in the different groups have non-identical nonlinear dynamics. To reduce the update frequency of event-triggered controller, a novel adaptive dynamic event-triggered communication scheme is presented based on the local stochastic sampled information. The proposed event-triggered conditions of the position state and velocity state have be given separately owe to their state ranges may be different, which lead to the position state and velocity state with different event-triggered instants and release intervals. The event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered conditions, the given event-triggered conditions are detected only at discrete sampled times, which means Zeno behavior can be excluded. A novel distributed protocol is designed based on the neighboring agents information of the position state and velocity state at event-triggered instants. The group consensus issue can be transformed into the convergence problem of the augmented error system. Then some mean-square group consensus criteria can be derived with the help of tools from graph theory and matrix analysis, and the event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the proposed transmission scheme. [ABSTRACT FROM AUTHOR]

This paper discusses the prescribed-time synchronization (PTs) issue in networks of piecewise smooth (PWS) systems. Firstly, two new lemmas with respect to the prescribed-time stability are developed for nonlinear PWS systems, where the stable time can be preset arbitrarily, and is irrelevant to any control parameters and initial values. Secondly, a feedback controller and a novel event-triggered controller are designed to realize PTs objective, respectively. Different from the existing linear dynamic event-triggered condition, the adjustable internal dynamic variable is governed by a nonlinear system, which is related to the prescribed time. Thirdly, by adopting set-valued analysis technique and generalized Lyapunov functional approach, the conditions of PTs are achieved in terms of linear matrix inequalities (LMIs). Finally, two application examples to chaotic Sprott circuit are provided to certificate the correctness of the obtained results and the effectiveness of the designed control schemes. • Two prescribed-time stability lemmas are established for piecewise smooth systems. • The convergence time can be arbitrarily pre-set in advance. • A new dynamic event-triggered controller is proposed to achieve the PTs. • The adjustable internal dynamic variable is governed by a nonlinear system. • The adjustable internal dynamic variable is related to the prescribed-time. • The generalized Lyapunov functional and the set-valued analysis approach are used. • The prescribed-time synchronization conditions are obtained in terms of LMIs. [ABSTRACT FROM AUTHOR]

In this paper we study a novel mathematical model with intraspecific and interspecific competition between two species consisting of a non-linear parabolic–ODE–parabolic system. It describes the evolution of two populations in competition for a resource, one of which is subject to chemotaxis. We analyze the local stability of the constant equilibrium solutions and we obtain the periodic behavior of the solution for certain data of the problem. For this purpose, we apply the meshless numerical method of Generalized Finite Differences (GFDM) and we prove the conditional convergence of the discrete solution to the analytical one. The conditional convergence of the numerical method is demonstrated and, thought its implementation, we obtain numerical solutions whose asymptotic behavior agrees with the analytically one expected. We give several numerical examples on the applications of this meshless method over regularly and irregularly distributed nodes to illustrate its potential. [ABSTRACT FROM AUTHOR]

This paper mainly proposes a novel stability condition for distributed order composite systems with delay based on some properties of Caputo fractional-order derivatives in distributed order form that we extend and the generalization of a new method of vector Lyapunov function combined with M-matrix. First, we extend some properties of the Caputo fractional-order derivative to its distributed order form of it effectively. Next, we use a new method to solve the stability problem of the distributed order systems via a series of class − κ functions. Then, we propose the novel stability condition of the distributed order composite systems whose interconnect part is not only linear but also nonlinear based on the generalization of a new method which is vector Lyapunov function combined with M-matrix. Moreover, we solve the stability problem of the distributed order composite systems with time-delay. Finally, we provide several numerical simulation examples for all different cases show the correctness and usefulness of the novel stability condition. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the "explosion of complexity" problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method. [ABSTRACT FROM AUTHOR]

This paper investigates the variable gain impulsive observer design problem for Lipschitz nonlinear systems. It is assumed that the measurements are contaminated by noise and received by observer at aperiodic instants. To establish a tractable design condition for impulsive observers, the piecewise linear interpolation method is used to construct the variable gain function. To quantify the impact of the measurement noises and exogenous disturbance on the estimation error, a Lyapunov-based condition for establishing exponential input-to-state stability (EISS) property of the observation error dynamics is presented. Then it is shown that the EISS condition can be expressed as a set of linear matrix inequalities (LMIs) by introducing a piecewise quadratic Lyapunov function. A convex optimization problem is proposed in which the EISS gain is minimized. Comparisons with the existing methods show the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]