Search

This paper studies the fixed-time stochastic synchronization problem of multi-weighted complex dynamical networks with impulsive effects. Different from most of previous networks, stochastic disturbances and impulsive effects are considered in this model. The non-chattering controller is utilized, and by devising a novel time-dependent Lyapunov function and dividing the impulsive intervals, a new sufficient criterion for the fixed-time stochastic synchronization (FDTSS) of multi-weighted complex dynamical networks (MWCDNs) is obtained. Secondly, compared with some existing results, this paper proposes a novel means of calculating the settling time by constructing comparison systems and exploiting the method of the classification discussion, and the settling time does not depend on the initial values of the system. In addition, compared with the existing fixed-time and finite-time controllers, the controller devised in this paper is continuous and do not involve sign functions, which non-chattering phenomenon in practical applications. Finally, the Lorenz system is submitted to certify the justifiability of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study a projective multi-synchronization problem for fractional-order complex-valued coupled multi-stable neural networks (FCVCMNNs) with time-delays. Using a complex decomposition approach, FCVCMNNs are divided into their real and imaginary components. Our method uses certain conditions for each subnetwork to achieve the multiple local equilibrium points or stable periodic orbits that are exponentially stable, which, when combined with the Lyapunov functions method, result in FCVCMNNs that are projectively multi-synchronized. The FCVCMNNs, on the other hand, are examined directly through the use of the Lyapunov functional method and linear matrix inequality (LMI). Various new sufficient conditions in the form of complex-valued LMIs are presented for the projective multi-synchronization of the considered FCVCMNNs. As a final step, we provide two numerical simulations to verify the effectiveness of the main results derived in this paper. [ABSTRACT FROM AUTHOR]

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of linear systems and nonlinear control systems through the lens of bilinear control systems. The key idea of these methods lies in the transformation of the coordinates of the nonlinear system into the Koopman observables, which are coordinates that allow the representation of the original system (control system) as a higher dimensional linear (bilinear control) system. However, for nonlinear control systems, the bilinear control model obtained by applying Koopman operator based learning methods is not necessarily stabilizable. Simultaneous identification of stabilizable lifted bilinear control systems as well as the associated Koopman observables is still an open problem. In this paper, we propose a framework to construct such stabilizable bilinear models and identify their associated observables from data by simultaneously learning a bilinear Koopman embedding for the underlying unknown control affine nonlinear system as well as a Control Lyapunov Function (CLF) for the Koopman based bilinear model using a learner and falsifier. Our proposed approach thereby provides provable guarantees of asymptotic stability for the Koopman based representation of the unknown control affine nonlinear control system as a bilinear system. Numerical simulations are provided to validate the efficacy of our proposed class of stabilizing feedback controllers for unknown control-affine nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural network (NN) optimized control strategy is presented to improve the inherent tradeoff between ride comfort of passengers and the suspension travel for full vehicle active suspension system with state constraints. To the best of our knowledge, the automotive suspension system control using hydraulic actuators is a highly complex nonlinear control task, involving external disturbances and uncertainties. To address it, this paper develops the virtual and actual optimal controllers based on backstepping technique and the identifier-actor-critic structure. Meanwhile, the Barrier Lyapunov functions are developed to prevent the systems from the state constraints and the systems states are limited in the preselected compact sets. It is particularly worth mentioning that the proposed optimal control strategy ensures that all the closed-loop signals remain bounded, while the power of the control input as well as the amplitude of the vertical displacement has been minimized. The simulation results show how the full-car system can be controlled optimally and satisfactorily, and confirm the superiority of proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of adaptive tracking control for multi-agent systems subject to output constraint and unknown hysteresis. Different from most existing results that use the barrier Lyapunov function and integral barrier Lyapunov function to solve the output constraint problem, the transformation technique is introduced in this paper, which can convert the original system to a constrained or completely unconstrained system. The difficulty caused by unknown Bouc-Wen hysteresis is solved via the Nussbaum gain technique. The continuous unknown function is estimated by using the radial basis function neural networks. The tracking differentiator is utilized to overcome the difficulty of "explosion of complexity". By using the Lyapunov stability theory, it is indicated that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Eventually, the feasibility of the designed approach is demonstrated by some simulation results. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating discrete-time fractional-order delayed quaternion-valued neural networks (DFDQNNs) by utilizing direct quaternion approach. Firstly, a novel lemma and its two corresponding corollaries have been proposed for estimating nabla fractional difference of the quaternion-valued Lyapunov function. Then, the existence and uniqueness of equilibrium point for DFDQNNs is proved by constructing a new quaternion-valued contraction mapping. In addition, by means of our designed Lyapunov functions and the effective feedback controller as well as neoteric nabla difference inequalities, some sufficient criteria have been obtained to ensure the global Mittag–Leffler stability and Mittag–Leffler synchronization of DFDQNNs, respectively. Finally, some numerical examples are provided to verify the yielded results. [ABSTRACT FROM AUTHOR]

In this paper, the multiple asymptotic stability is investigated for fractional-order quaternion-valued neural networks (FQVNNs) with time-varying delays. The activation function is a nonmonotonic piecewise nonlinear activation function. By applying the Hamilton rules, the FQVNNs are transformed into real-valued systems. Then, according to the Brouwer's fixed point theorem, three new conditions are proposed to ensure that there exist 3 4 n equilibrium points. Moreover, by virtue of fractional-order Razumikhin theorem and Lyapunov function, a new condition is derived to guarantee the FQVNNs have 2 4 n locally asymptotic stable equilibrium points. For the first time, the multiple asymptotic stability of delayed FQVNNs is investigated. Contrast to multistability analysis of integer-order quaternion-valued neural networks, this paper present different conclusions. Finally, two numerical simulations demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive neural network (NN) optimal control problem for a permanent magnet synchronous motor (PMSM) system. The addressed PMSM system contains unknown nonlinear dynamics and constraint states. The neural networks (NNs) are employed to identify the unknown nonlinear dynamics and by constructing barrier performance index functions and barrier Lyapunov functions, an adaptive NN optimal control method is developed under the framework of the actor-critic architecture and backstepping control technique. It is proved that the presented optimal control strategy can not only ensure the closed-loop system stable, but also guarantee the angular velocity, stator current and other state variables of PMSM are within given bounds. Furthermore, it can minimize the performance index functions. The effectiveness of the developed NN adaptive optimal controller is verified by computer simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an inverse optimal composite control (IOCC) method to solve the optimization problem for a class of high-dimensional nonlinear strict-feedback systems with disturbances. Initially, we give these systems an inverse optimal control framework that avoids solving Hamilton–Jacobi-Bellman equations. Then, a nonlinear disturbance observer is designed to estimate the disturbances in the systems. We incorporate these disturbance estimates into the virtual control law design through a backstepping method that gives us a control Lyapunov function. In the end, this control Lyapunov function is utilized to obtain a composite controller that achieves optimality and disturbance rejection. We provide rigorous proofs for the convergence of the proposed composite controller. Simulation studies and comparative results from a real-life application to single-link robots show that the proposed composite controller achieves more robustness and effectiveness than the popular control methods in high-dimensional nonlinear systems. [ABSTRACT FROM AUTHOR]

The bumpless transfer consensus control problem for linear homogeneous multi-agent systems subject to agent-dependent switching directed communication topologies is investigated in this paper. According to the information of graph Laplacian matrix and relative state of agent, we propose a novel agent-dependent switching law to guide the switching among these topologies, then the leader-following consensus performance of multi-agent systems is achieved via using the multiple Lyapunov functions method. Further, since the switching consensus controllers are considered, the control signal bumps are inevitable at switching instants, and some sufficient conditions via linear matrix inequalities are developed to pursue the bumpless transfer performance of multi-agent systems. Besides, the agent-dependent switching law also allows the error dynamics under each directed subtopology to be unstabilizable. Finally, the theoretical results are verified by two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper investigates the formation containment control under sampling and with time delays for multi-agent systems (MASs). First, a novel sampling control protocol for the MASs to achieve formation containment is proposed, where the communication among agents is only occurred at the sampling instance. Then the communication load and the waste of energy can be decreased significantly. In addition, time delays are considered in this paper. Second, by establishing an appropriate Lyapunov function, sufficient conditions for MASs with sampled data and time delays reaching formation containment are obtained by handling the established Lyapunov function. Finally, the obtained results are demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability of conformable fractional-order nonlinear differential systems with time-varying delay and impulses. The authors utilize the principle of comparison and the Lyapunov function method to establish sufficient conditions that guarantee the exponential stability of a specific class of conformable fractional-order nonlinear differential systems. These findings extend the existing results on systems with integer-order to a certain extent. Furthermore, the paper considers the effect of impulses in the delayed system, which was not addressed in previous literature The authors also apply the criterion for exponential stability to conformable fractional-order neural networks. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural network (NN) constrained fault-tolerant control (FTC) method is proposed for a class of nonlinear pure feedback systems with actuator faults and state constraints. By designing a fault-tolerant compensation controller and a new asymmetric time-varying tangent Barrier Lyapunov function (ATVTBLF), the problem of time-varying asymmetric state constraints caused by actuator failure is solved. The actuator takes into account both loss of effectiveness and bias fault. Different from the existing asymmetric BLF, the new BLF solves the problem of asymmetry under tangent constraints and expands the application range of the asymmetric constraint. NN is used to approximate the unknown items generated in the process of designing fault-tolerant controllers. Based on the Lyapunov stability analysis, it is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and all states do not violate the bounds. Finally, the simulation example verifies the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive asymptotic tracking controller for uncertain nonstrict-feedback nonlinear systems(NFNSs) with full-state constraints and unknown actuator failures. By constructing a class of new switched high-order barrier Lyapunov functions(BLFs) candidates to the backstepping design, the asymptotic tracking performance can be guaranteed, all states do not violate constraints. The neural networks(NNs) is used to handle the difficulties caused by the unknown nonlinearities, the event-triggered control law based on relative threshold method for reducing the communication load between the controller and actuator. The control scheme guarantees that all closed-loop signals of the system are bounded and the tracking error asymptotically approaches a pre-defined bound, no matter whether the actuators operate in normal or faulty modes and the number of actuator failures can be infinite. Finally, simulation results including numerical simulation and practical application simulation verify the feasibility of the control scheme. [ABSTRACT FROM AUTHOR]

In this paper, finite-time adaptive control (FTAC) is investigated for non-affine uncertain constrained nonlinear systems with actuator faults. The state constraints are dealt with by using nonlinear mapping (NM), and an auxiliary dynamical signal is used to handle the unknown dynamic uncertainties of the system. Based on the converted system, a FTAC strategy is designed via command filtered backstepping method. By introducing the compensation signals and adding them into the whole Lyapunov function, and with the help of the defined compact set in stability analysis, it is strictly proved that all signals are semi-globally practical finite-time stable (SGPFS) and all the states are within the specified open set. Simulation results verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies the neural network (NN) decentralized observer-based fault-tolerant control (FTC) design problem on the nonlinear interconnected fractional-order systems. The considered fractional-order systems have the non strict-feedback form and are subject to immeasurable states and intermittent actuator faults. Neural networks (NN) are employed to identify the unknown dynamics, and a NN decentralized observer is formulated to estimate unknown states. By constructing appropriate Lyapunov functions and using the backstepping dynamic surface control (DSC) technique, a NN observer-based decentralized FTC method is developed. It is proved that the developed NN decentralized FTC scheme can guarantee that the controlled interconnected fractional-order system is stable and the track errors can be made smaller. Finally, a practical simulated example is provided to check the validity of the NN decentralized FTC algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem of inertial neural networks (INNs) with time delays by virtue of event-triggered (E-T) impulsive control, in which a Lyapunov function based E-T mechanism is used to determine impulsive instants. The synchronization analysis of INNs through E-T impulsive control technique unlike time-triggered impulsive control, which would be activated when certain well-designed conditions exist, E-T impulsive control is only allowed when certain well-defined events occur. Besides that, control input is only required at triggered instants and also no control input is required for two triggered instants in a sequence. Considering the E-T mechanism, the synchronization analysis of the INNs is discussed by reduced and non-reduced order approaches and constructing the suitable Lyapunov functionals. Finally, two simulation results are provided to illustrate the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

The problem of tracking uncertain target is interesting and challenging. This paper studies the target tracking control problem of Euler–Lagrange system with unknown target trajectory. Fourier series and neural network are utilized to reconstruct the target trajectory, which is mathematically linked with the actual camouflaged target trajectory and facilitates the design and analysis. An error transformation function is introduced and embedded with the Lyapunov function, with which an adaptive tracking control scheme is developed. It is shown that such strategy is able to ensure the tracking error converging to a prescribed compact set containing the origin at a self-defined convergence rate. The simulation results verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo's fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper addresses the global exponential stability of a class of quaternion-valued neural networks (QVNNs) with mixed delays including time-varying delays and infinite distributed delays. Because of the noncommutativity of quaternion multiplication, the concerned quaternion-valued models separated into four real-valued parts to form the equivalent real-valued systems. Based on M-matrix properties and homomorphism mapping theories, some sufficient conditions are derived to guarantee the existence and uniqueness of the equilibrium point of the system. Conditions for ensuring the global exponential stability of the equilibrium point of the system are obtained on the basis of the vector Lyapunov function method instead of the linear matrix inequality method. Using a similar method, the mixed-delay QVNNs with parameter uncertainties are also studied, and the conditions for ensuring the global robust exponential stability of the system are established directly. The adopted approach and the obtained results in this paper complement already the existing ones. Finally, three numerical examples are provided to illustrate the feasibility and the less level conservatism of the main results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control scheme is investigated for a medium scale unmanned autonomous helicopter (UAH) with unknown external disturbances and system uncertainties to achieve improvement on the flight performance. The neural networks (NNs) are employed to compensate the system uncertainties. The second-order disturbance observers are introduced to restrain the compound disturbances which are combined with the NN approximation errors and the external disturbances. Accordingly, the tracking control law is designed for the UAH. The closed-loop stability of the whole UAH system is proved by using Lyapunov function method. Simulation results show that the developed control scheme can effectively solve the tracking control problems of UAH and certainly accomplish strong robustness with respect to the external disturbances and system uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, by transforming the high-order system into the system with vector-matrix form, the authors employed variational methods in Sobolev spaces, Lyapunov function method, Dynkin's formula and comparison principle to deduce the stochastic input-to-state stability in mean square on the high-order time-delays reaction-diffusion neural networks under the concise event-triggered mechanism. Remarkably, it is the first paper in which the LMI-based criterion of input-to-state stability of time-delays high-order reaction-diffusion neural networks with event-triggered control is derived, in which the diffusion item plays its role. Not similarly as those of previous literature, the sufficient conditions of the main result in this paper are not involved to Lyapunov function, which implies that the conditions of this paper is easier to be verified than ever. With the help of computer Matlab LMI toolbox, a numerical example illustrates the effectiveness of proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, exponential stability of stochastic complex-valued dynamical networks with hybrid impulses is considered. Therein, different from the existing works on the moment stability of stochastic complex-valued systems, almost sure exponential stability is studied, in which noise contributes to the stability of the system. Hybrid impulses, which allows that a kind of impulsive sequence includes stabilizing and destabilizing impulses simultaneously, are first exerted on stochastic complex-valued networks. In light of Lyapunov method, stochastic analysis theory, average impulsive interval and average impulsive gain, we establish improved almost sure exponential stability criteria under the two situations that average impulsive interval T a satisfies T a < + ∞ and T a = + ∞ separately. The stability criteria we addressed possess two characteristics as follows. Firstly, time-derivatives of the Lyapunov functions are permitted to be indefinite, even unbounded, based on indefinite Lyapunov functions, which results in lower conservative consequence. Secondly, it is worth noting that the mutual restrains among average impulsive gain, average impulsive interval and the noise intensity are represented in the improved criteria. Besides, the theoretical results are directly applied to study the stability of stochastic systems with aperiodically intermittent noise. Finally, an application to inertial complex-valued neural networks and several numerical examples are provided to show the feasibility and advantages of the theoretical results. [ABSTRACT FROM AUTHOR]

Affected by multiple operation conditions, wastewater treatment process (WWTP) is a complex industrial process with strong nonlinearity and disturbance. How to enhance the rapid tracking response-ability and robustness of the controller is still a challenge when the operation conditions change. To solve this problem, a type-2 fuzzy broad learning controller (T2FBLC) is proposed in this paper. First, a type-2 fuzzy broad learning system (T2FBLS) is constructed in T2FBLC by replacing nodes in feature window with a group of interval type-2 fuzzy submodules. Then, the proposed T2FBLC can take tracking error as inputs while its outputs acting on WWTP to directly obtain a control law, and the controller makes a quick tracking response in different operation conditions. Second, the weight parameters of T2FBLC are adjusted by using the gradient descent method to ensure the control performance. In this way, the developed T2FBLC can realize online learning to reduce tracking errors. Third, according to the Lyapunov function theory, the stability of control strategy is proved. Finally, benchmark simulation model 1 (BSM1) is adopted to verify the effectiveness of T2FBLC. The experimental results prove the applicability and superior tracking performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel prescribed finite-time output feedback control scheme for quadrotor trajectory tracking control. The proposed control scheme considers the quadrotor modeling containing uncertain nonlinearities and strong coupling. The neural observer is set up to estimate the unknown state variables. The main difficulty caused by the time-vary coefficient matrix to design a state observer is overcame by the convex combination technique. To get a prescribed finite-time tracking performance, Barrier Lyapunov Function (BLF) approach is presented for control design. The constructed controllers guarantee that the tracking errors meet the prescribed accuracy in a pre-specified finite settling time. Finally, a simulation example verifies the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This paper considers the fixed-time tracking control problem for system-constrained nonlinear pure-feedback systems involving input saturation and output constraints. A sequence of auxiliary virtual and actual input signals is designed to obtain an expression for the system tracking error and stabilize the system. A combination of the fixed-time stability theory, barrier Lyapunov function, and radial basis function neural network is employed to develop the proposed method for obtaining the expected performance from the considered system. Further, a theorem is proposed to ensure that the designed controller allows the system output to track the reference signal within a fixed time, ensuring that the tracking error is limited to a small neighborhood of origin within a fixed time and that all the signals in the system are bounded. The aforementioned problem can be solved using the proposed control method, and the simulation experiments indicate the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

This paper proposes a finite-time adaptive neural network (NN) position tracking control method for the permanent magnet synchronous motor (PM SM) servo system with full-state constraints. NNs are utilized to compensate the parameter uncertainties and load torque disturbances of the PMSM servo system. Multiple barrier Lyapunov functions are introduced in the backstepping based control design, such that the rotor position, the rotor angular velocity and the currents of the d-q axis are constrained in given compact sets. In addition, the finite-time control technique is adopted to the control design, which can accelerate the convergence speed and improve the robustness of the PMSM servo system. Under the proposed control algorithm, the position tracking control is realized in finite time, and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results are presented to show the effectiveness of the developed control approach, and some comparisons are given to show the rapid and accurate position tracking control performance. [ABSTRACT FROM AUTHOR]

• The SPFTS scheme is applied to deal with the consensus issue for nonstrict nonlinear MASs. With the help of the proposed strategy, an adaptive NN fixed-time controller is devised to ensure the consensus of MASs. Compared with the finite-time control, the convergence time of the fixed-time consensus control doesn't depend on the initial values. • Full state constrains and input delay are first considered in nonstrict uncertain MASs. By using the backstepping technique, the barrier Lyapunov functions are created to overcome the difficulties caused by full state constraints and the method of Pade approximation is adopted to eliminate the influence of input delay. Then, the output trajectories of followers can track with the signal of the leader in fixed time. • A novel stability analysis method is developed to solve fixed-time consensus problem for for nonlinear nonstrict uncertain MASs in this note. This paper concentrates on a fixed-time consensus issue for nonstrict nonlinear uncertain multi-agent systems (MASs) with state constraints and input delay. In comparison with previous works, the topic of full state constraints and input delay is first embodied in nonstrict MASs in a fixed time. A semi-global practical fixed-time stability (SPFTS) is employed to handle the consensus problem in this note. The radial basis function neural networks (RBFNNs) are developed to counteract unknown items in each agent. Pade approximation approach is introduced to cope with input delay. By using the backstepping technique, adaptive virtual controllers, adaption laws and the actual consensus controller are devised. And the rest followers can converge to a specified trajectory built by the leader in fixed time. Finally, a practical example is employed to test the correctness for the proposed control protocol. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotical synchronization of fractional-order complex neural networks with non-delayed and delayed couplings is investigated. By employing the Kronecker product technique and weighted norm, two Lyapunov functions are constructed. Based on the fractional-order Lyapunov direct method and Kronecker product method, together with the Laplace transform and the comparison principle, several novel sufficient conditions on synchronization of fractional-order complex neural networks with non-delayed and delayed couplings, respectively, are proposed. Finally, three numerical examples are given to show the effectiveness of our proposed theoretical results and the difference between our main result and some existing results in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed consensus control for a group of autonomous marine vehicles with nonlinearity and external disturbances via sampled-data communications. First, the kinematical equation of autonomous marine vehicle is established. Second, stability criteria is derived to ensure the stability of autonomous marine vehicles by combining Lyapunov function method and free-weighting matrix approach. Third, a distributed sampled-data control strategy is proposed to achieve the consensus of autonomous marine vehicles by designing suitable control parameters. Numerical simulations are provided to verify the effectiveness of the proposed consensus control approach. [ABSTRACT FROM AUTHOR]

This paper focuses on a tracking control issue for a class of uncertain switching nonlinear systems under arbitrary switching with unknown time-varying parameters. An approximator is designed by combining Multilayer neural network (MNN) with Fourier series expansion (FSE) to approximate the nonlinearly parameterized unknown functions. Then, a common Lyapunov function (CLF) is constructed and a novel adaptive neural network (NN) control scheme is proposed by using the adaptive Backstepping technique. It can be proven that the tracking error falls into a prespecified domain of equilibrium and the whole system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the designed approach is verified through two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy control scheme is addressed for switched nonlinear systems with uncertain dead-zone, unknown nonlinearities and immeasurable states. A novel proposed mode-dependent fuzzy dead-zone model (MFDM) can not only describe the uncertain dead-zone, but also overcome the common fuzzy dead-zone model (CFDM) problems caused by disconnected parameters and conservativeness. The unknown functions are approximated by fuzzy logic systems. To estimate the immeasurable states, a switched fuzzy state observer is constructed. By using multiple Lyapunov function and defuzzifying for MFDM, a new mode-dependent fuzzy controller is proposed to assure the boundedness of the closed-loop system and the desired tracking performance. The feasibility of the presented control technique is proved by simulation examples. [ABSTRACT FROM AUTHOR]

This paper focuses on stability and synchronization of fractional-order Hopfield neural networks. By taking information on activation functions into account, two novel convex Lyapunov functions are constructed: one is a fractional-order-dependent Lyapunov function, and the other is a new quadratic Lyapunov function. Based on these two Lyapunov functions, together with a fractional-order differential inequality, a fractional-order-dependent Mittag–Leffler stability criterion is derived for fractional-order Hopfield neural networks, which is in the form of linear matrix inequalities (LMIs). Moreover, a Mittag–Leffler synchronization criterion in terms of LMIs is presented for drive-response fractional-order Hopfield neural networks under linear control. Finally, three numerical examples are provided to indicate the benefits and less conservatism of the obtained criteria in this paper. [ABSTRACT FROM AUTHOR]

Highlights • The input is no longer a single frame, but a sequence of several adjacent frames. • A CRNN module is proposed, which is basically the same as the standard RNN, except that it uses convolutional connection. • When the difference in the feature image of a certain layer is large, it is better to add CRNN / RNN after this layer. • Our method has the lowest error of output compared to the current state-of-the-art methods. Abstract Hand pose estimation plays an important role in human–computer interaction. The traditional way is to deal with a video stream frame by frame. However, since the gesture in the video is changing continuously, the adjacent frames must be highly related to each other. Therefore, the input of the neural network in this paper was set to be a series of contiguous video frames in order to make use of the relevance that the adjacent frames have. In this paper, a convolutional recurrent neural network (CRNN) module is proposed, which combines the characteristics of Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN), and can significantly improve the accuracy of the network.The impact of the location of the CRNN/RNN module in the network is also discussed in this paper. Finally, we demonstrated that our approach significantly outperforms the current state-of-the-art techniques in the NYU Hand dataset. [ABSTRACT FROM AUTHOR]

This paper addresses the consensus control problem for a class of multi-agent systems with distributed parameter models, and all the agents in the considered systems are governed by the one-dimensional parabolic equations or the one-dimensional second-order hyperbolic equations. The main contribution of this paper is to apply Lyapunov functional approach to the multi-agent systems with distributed parameter models, and solve the consensus control problem of such multi-agent systems on an appropriate Sobolev space. The distributed consensus-based feedback control protocols are obtained based on the virtual leader approach, and when the feedback control laws are applied to the systems, consensus on L 2 (0, 1) space (corresponding to the parabolic equations) or on W 1, 2 (0, 1) ×  L 2 (0, 1) space (corresponding to the hyperbolic equations) is achieved for all the directed communication graphs with spanning trees. Simulation examples illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The stability analysis of time-delay neural networks with reaction-diffusion terms in the sense of Riemann–Liouville derivative is still an open problem, which will be considered in this paper. We first extend a new inequality on Riemann–Liouville fractional-order derivative, which plays an important role in the subsequent proof. Using the Lyapunov direct method, Jensen's integral inequality, and the linear matrix inequality (LMI) method, several easy-to-test criteria expressed by system parameters and given parameters are given to ensure the stability of the system under consideration. The advantage of our method is that we can directly calculate the integral-order derivative of the Lyapunov function, which can be very convenient to test the stability of practical system. Finally, the validity and conciseness of the results are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, an observer-based adaptive fixed-time control strategy is put forward for uncertain nonstrict-feedback nonlinear systems subject to prescribed performance, full-state constraints and event-triggered mechanism. The difficulty of control design is to use the state observer to estimate unmeasurable states for nonstrict-feedback form in the fixed-time convergence setting. Neural networks are implemented to model the unknown nonlinearities of system. Via introducing fixed-time theory and asymmetric barrier Lyapunov function (ABLF), the fixed-time control problem of the full-state contrained nonlinear system with prescribed performance is solved. Meanwhile, the problem of "explosion of complexity" caused by backstepping technique is averted by utilizing the dynamic surface control technique. Furthermore, an event-triggered controller is devised, which can significantly save communication resources. Moreover, it is concluded that all signals involved are bounded, full-state constraints are not transgressed, tracking error remains within a prescribed domain and Zeno phenomenon is completely circumvented. Finally, the effectiveness of the proposed algorithm is verified by some simulation results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of fuzzy controller for networked control systems (NCSs). T-S fuzzy system approach is adopted to study the problem. In account of NCSs, various data missing on both sides of the controller caused by event-triggered scheme, data losses and event-driven controller are involved. For handling this issue, an auxiliary random series method is presented to describe the data transferring in the network. Based on this method, the closed-loop NCSs is constructed and then analyzed via Lyapunov stability theory. Additionally, the probability of random data losses at each instant is supposed to be different which is more practical. For the purpose of obtaining more relaxed stabilization conditions, the fuzzy Lyapunov function obtained on the basis of both plant and controller fuzzy rules is employed. Furthermore, variations of membership functions are taken into account, and consequently, slack matrices are introduced to obtain less conservative result. At last, by considering a cart-damper-spring system, the effectiveness of the proposed method is illustrated. [ABSTRACT FROM AUTHOR]

This paper investigates the controller design for the tracking problem of uncertain nonlinear systems with constraints on input and output. First, to avoid the full-state measurement, the high-gain observer is designed to estimate the unmeasured state. Compared to existing observer design for nonlinear systems, the high-gain observer design only requires a modified version of the Lipschitz condition. The output feedback controller is further presented on this basis. Second, to consider the transient constraints on the tracking performance, a barrier Lyapunov function with the user-defined time-varying performance is developed. In addition, the proposed controller design is shown to be free of control direction singularity. The convergence of the learning scheme and the boundedness of all the closed-loop signals during the learning phase are discussed theoretically. Finally, two simulation examples are conducted to verify the advantage of the proposed adaptive output feedback controller design. [ABSTRACT FROM AUTHOR]

This paper studies the global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. By introducing the complex-valued Filippov differential inclusion, we construct the framework of studying the dynamical behaviors of complex-valued neural networks with discontinuous bivariate activation functions. By employing the Leray–Schauder alternative theorem and choosing an appropriate Lyapunov function, we prove the global exponential stability of delayed complex-valued neural networks with discontinuous activation functions. The numerical example provided shows the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper explores finite-time (F-T) synchronization for a type of fully complex-valued (C-V) networks with or without delays by proposing intermittent control schemes but without using the ordinary separation technique. Above all, the vector signum function in complex field is proposed as the generalization of real-valued counterpart, which is critical to the control design in complex field and the construction of Lyapunov functions. To realize F-T synchronization, several complex-valued intermittent controllers, only dependent of the information of controlled nodes, are designed on the addressed complex-valued networks, which are different from the design on the divided real-valued subsystems. In the theoretical analysis, some nontrivial Lyapunov functionals and functions are constructed by virtue of the proposed signum functio n and some inequalities are developed in complex domain to establish criteria of F-T synchronization. Finally, some numerical examples are performed to reveal the effectiveness of the derived results and the practicality of the proposed control strategies. [ABSTRACT FROM AUTHOR]

This paper studies the distributed leader-following consensus control problems of position-constrained multiple Euler-Lagrange Systems (ELSs) with unknown control directions. The objective of our discussion is to develop a consensus protocol despite the existence of position constraints and unknown control directions in each agent. Most of the existing works related to state constraints are for single systems and rare results are concerned about multi-agent systems. With the help of the barrier Lyapunov function, Nussbaum gain adjusting technique, and adaptive control methodology, a novel leader-following consensus algorithm is successfully designed to make sure the convergence to zero of the consensus errors and the boundedness of the signals in the closed-loop system. Moreover, the position constraints for each agent are never violated for all time during the control process. The effectiveness of the main result is illustrated by a practical mechanical system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the quasi-synchronization issue of an array of Diffusion Effects Neural Networks (DENNs) with time-varying coupling strength. Two kinds of quasi-synchronization scenarios are discussed. One is self-synchronization and the other is tracking-synchronization. In order to lower the communication loads and reduce the control resource consumption, we propose a new control scheme called intermittent control of reginal division to make the synchronization error within a bounded scope. In this novel control scheme, the non-negative real region is divided into three subregions in advance and an auxiliary Lyapunov function is imported to decide the work time and the rest time by its relationship with three subregions. Moreover, by using rigorous mathematic analysis, we obtain sufficient conditions for the two kinds of quasi-synchronization modes of DENNs under the as-proposed control scheme. Nonidentical term in the network is viewed as external disturbance about to be compensated by the controller. The result shows that the upper bound of synchronization error will be progressively regulated by the parameters in chosen divided region. Several numerical examples are also presented to verify the validity of our theory. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive neural network prescribed performance synchronization scheme for unknown complex dynamic networks with different dimensions. Based on predefined performance bounded and Lyapunov stability theory, adaptive neural networks controllers are designed to ensure that synchronization errors remain in a neighborhood of origin with the prescribed bounds. In addition, the paper analyses in detail that the synchronization behaviors between drive network selected as the three-dimension chaotic system and response network selected as the four-dimension hyperchaotic chaotic system. The numerical simulation results are presented to show the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the stability analysis and observer-based controllers design for T–S fuzzy positive systems. A fuzzy copositive Lyapunov function is first proposed to analyze the stability of the T–S fuzzy positive systems via linear programming. In terms of the property of the fuzzy membership functions, the fuzzy copositive Lyapunov function is employed to derive the less conservative stability conditions. Then, the line-integral Lyapunov function is presented for the stability analysis. The time-derivatives of the membership functions do not appear in the stability analysis of the T–S fuzzy positive systems, therefore, the proposed stability conditions are more relaxed than those of the conventional Lyapunov function approaches. Based on the obtained stability conditions, observer-based control schemes are designed such that the resultant closed-loop systems are both stable and positive. Finally, two examples are provided to validate the effectiveness of the results proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we put in effort to inspect the passivity and exponential passivity problem of memristive neural networks with time-varying delays and reaction–diffusion term. Based on the basis of generalized Lyapunov approach, Poincar e ` inequality, Schur complement Lemma, free-weighting matrix approach as well as some inequality techniques, the main conclusions of this paper are derived in the form of linear matrix inequality (LMI). What is noteworthy is that the obtained sufficient criteria rely on the reaction–diffusion term, which implies that the reaction–diffusion term can effect the passivity of the given system. Finally, two numerical examples are emerged to check the practicability of the derived passivity conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time robust synchronization problem of mixed time-delayed neural networks (DNNs) with discontinuous activations and uncertain external perturbations. Two classes of simple discontinuous controllers (i.e., switching state-feedback controller and switching adaptive controller) are designed such that the response system can be finite-time robustly synchronized with a drive system. Without using the well-known finite-time stability theorem given by Forti in 2006, the finite-time robust synchronization control of discontinuous DNNs can be realized via generalized Lyapunov–Krasovskii functionals approach and novel analysis techniques. Moreover, the upper bounds of the settling time for synchronization are estimated. The main tools of this paper involve functional differential inclusion theory in the sense of Filippov solutions and non-smooth analysis. Finally, two numerical examples are provided to illustrate the effectiveness of the designed control method and the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with a class of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator. Using the differential inequality theory and Lyapunov functional method, a set of sufficient conditions which ascertains that the existence and exponential stability of anti-periodic solutions of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator are derived. Computer simulations are delineated to substantiate the correctness of our theoretical predictions. The obtained results of this paper are new and complement some earlier works. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time synchronization problem of nonlinear complex dynamical networks (NCDNs) on time scales. A pinning impulsive control strategy, in which only a small portion of nodes are impulsively controlled, is designed to achieve finite-time synchronization for NCDNs on time scales. Based on the theory of time scales, Lyapunov method and mathematical induction approach, a finite-time synchronization criterion is obtained for NCDNs on time scales under the pinning impulsive control strategy. It is shown that the finite-time synchronization criterion in this paper is different from that derived for continuous-time or discrete-time NCDNs. Moreover, the idea of this paper provides a unified approach to study the finite-time synchronization problems for continuous-time NCDNs and their discrete-time counterparts simultaneously. A numerical simulation example is given to illustrate the effectiveness of our result. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of global exponential stability for a class of memristive Cohen–Grossberg with mixed time delays and impulsive time window. Based on the memristor theory, impulse control theory, and mathematical induction method, stability criteria for the considered memristive Cohen–Grossberg neural networks are derived by employing appropriate Lyapunov functions. Compared with existing impulse control schemes, the impulse instants are extended to some bounded time intervals, we will show that the neural networks can still be stable under reasonable assumptions. Furthermore, the conditions obtained in this paper are easy to be checked, and they can be applied to improve previous results concerning stability for memristive neural networks. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]