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This article aims at this problem of adaptive neural tracking control for state-constrained systems. A general fixed-time stability criterion is first presented, by which an adaptive neural control algorithm is developed. Under the action of the proposed adaptive neural tracking controller, the tracking error converges into a small neighborhood around the origin in fixed time; meanwhile, all system states abide by the corresponding state constraints for all the time. The main difference between the present research and the previous control schemes for state-constrained systems is that this article proposes a novel and feasible approach to ensure that the constructed virtual control signals satisfy the state constraints on the corresponding states viewed as the virtual control inputs. Such an approach guarantees theoretically that all the system states cannot violate their constrained requirements at any time. Finally, two simulation examples provide support to the proposed results.

This article considers the problem of finite-time (FT) tracking control for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with input backlash. A modified FT command filter is designed in each step of backstepping, which ensures the output of the filter can faster approximate the derivatives of virtual signals, suppress chattering, and relax the input signal limit of the Levant differentiator. Then, the corresponding improved FT error compensation mechanism is adopted to reduce the negative impact of filtering errors. Furthermore, a neural-network-adaptive technology is proposed for MIMO systems with input backlash via FT convergence. It is shown that desired tracking performance can be implemented in finite time. The simulation example is presented to illustrate the effectiveness and advantages of the new design method.

This paper presents a new asymmetric Lyapunov-Krasovskii functional (LKF) method on the stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with time delay. For the reduction of conservativeness, combining the method with membership-function-dependent approach, we propose a novel delay-dependent stability condition in the form of linear matrix inequalities (LMIs). Based on the condition, we further obtain a novel condition of stabilization. At the end, we provide two numerical examples to verify the advantage of the stability and stabilization approaches, respectively.

This paper discusses consensus tracking issue for multi-agent systems (MASs), and the purpose is to develop a fixed-time consensus proposal by fuzzy adaptive method. To this end, we first set up a more general fixed-time stability criterion. By using the proposed stability criterion, a backstepping design procedure is presented to construct the fixed-time fuzzy adaptive controller. The suggested fuzzy adaptive control protocol guarantees that 1) for each agent its closed-loop signals keep bounded; 2) the consensus tracking error tends to a small region around origin in fixed time. In addition, the virtual control signals are constructed to be the piecewise functions to prevent the singularity of their derivatives. Curve fitting method is used such that the designed virtual control signals are derivable at the point of partition. At last, numerical simulation further checks the validity of the suggested control strategy.

In this paper, the structural controllability of leader–follower systems over digraphs is discussed. Firstly, with the aid of leader–follower partition, we analyze the topological characteristics of systems without dilations. Moreover, we divide the digraph into the leader subgraph and the follower subgraph. By analyzing the topological characteristics of the follower subgraph, a sufficient condition to ensure the system structurally controllable is given. Furthermore, some special topologies of follower graphs are analyzed, such as unidirectional cycle graphs and directed paths, and the corresponding sufficient conditions of structural controllability are given. Meanwhile, a method to construct digraphs with structural controllability is presented. Finally, the strong structural controllability of directed tree graphs is considered, as well as the selection mechanism of leaders and the lower bound of the number of leaders under strong structural controllability are given. The above results reflect the effects of topologies on strong (or weak) structural controllability.

The current paper addresses the fuzzy adaptive tracking control via output feedback for single-input single-output (SISO) nonlinear systems in strict-feedback form. Under the situation of system states being unavailable, the system output is used to set up the state observer to estimate the real system states. Furthermore, the estimation states are employed to design controller. During the control design process, fuzzy logic systems (FLSs) are used to model the unknown nonlinearities. A novel observer-based finite-time tracking control scheme is proposed via fuzzy adaptive backstepping and barrier Lyapunov function approach. The suggested fuzzy adaptive output feedback controller can force the output tracking error to meet the pre-specified accuracy in a fixed time. Meanwhile, all the closed-loop variables are bounded. Compared to some existing finite-time output feedback control schemes, the developed control strategy guarantees that the settling time and the error accuracy are independent of the uncertainties and can be specified by the designer. At last, the effectiveness and feasibility of the proposed control scheme are demonstrated by two simulation examples.

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.

In this paper, a novel asymmetric Lyapunov–Krasovskii functional (LKF) method for the stability of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay is proposed. This asymmetric LKF method is shown to effectively reduce conservatism compared with symmetric LKF method. For further improving the stability criterion, the method is combined with the improved membership-function-dependent technique. Two numerical examples are given to demonstrate the advantages of our method and stability criterion numerically.

This paper focuses on the problem of the fuzzy filtering for networked nonlinear interconnected systems based on decentralized adaptive event-triggered (AET) scheme. Firstly, a new decentralized AET scheme is proposed, and some unnecessary data packets are discarded through decentralized adaptive rule, thereby saving network communication resources. Secondly, the H ∞ performance analysis of the filter error system is presented by using the fuzzy line-integral method, which does not need to give the time derivative upper bounds of the membership function in advance. Then, the combination of the Wirtinger-based inequality and the extended reciprocally convex matrix inequality is used to establish sufficient conditions for the filter error system to meet H ∞ performance. Moreover, a method for jointly designing the distributed AET parameters and fuzzy filter parameters is proposed. Finally, two examples are given to verify the effectiveness of the proposed method.

This article is aimed at developing a finite-time adaptive fuzzy control strategy for a class of nonlinear strict-feedback systems. For the first time, a fast finite-time practical stability criteria is set up, which provides an effective approach to address the finite-time adaptive fuzzy control design. Furthermore, a systematic finite-time adaptive fuzzy control design procedure is developed by embedding that practical stability criteria. The closed-loop stability analysis shows that the tracking error converges to a small region around the origin in finite time. Meanwhile, all the signals in the closed-loop system are bounded. At last, the presented results are tested by a numerical example.

In this article, an adaptive fuzzy control scheme based on command filtering is proposed for the position tracking control of permanent magnet synchronous motor (PMSM) stochastic system with full state constraints. Firstly, fuzzy logic systems are employed to approximate unknown stochastic nonlinear functions in PMSM stochastic system. Then, the barrier Lyapunov functions are constructed to ensure that all states of the system do not violate its constrained boundary. In addition, the problem of “explosion of complexity” in traditional backstepping design is solved by using the command filtering technique and the error compensation mechanism is introduced to reduce filtering errors. At last, the effectiveness of the scheme is illustrated by simulation results.

This paper addresses adaptive neural output feedback control for uncertain nonlinear switched systems. The main difficulty for control design comes from the loss of the precise information on those virtual coefficients of each subsystem. To overcome this difficulty, we give a robust observer design scheme by using convex combination approach. Furthermore, develop an observer-based output feedback control strategy. During the procedure of control design, adaptive neural control approach is used to deal with the unknown nonlinear functions and backstepping technique is employed to construct the ideal control laws. It is shown that the presented control law achieves the control issue of getting small tracking error, meanwhile, ensuring boundedness of all the closed-loop signals. Finally, a simulation example is used to test our results.

For a class of nonstrict-feedback nonlinear large-scale systems with input delay, saturation and unknown virtual control gains, we propose a decentralized output-feedback control scheme in this paper. In the process of control design, a novel auxiliary system is proposed to overcome the difficulty caused by time-varying input delay. The convex combination technique is used to overcome the difficulty caused by unknown virtual control gains, and further construct the state observer. Then a decentralized output-feedback controller is designed by using the adaptive neural backstepping control approach. By Lyapunov stability theory, it is proved that the proposed decentralized output-feedback controller can ensure that tracking errors converge to a small neighborhood of the origin and other closed-loop states are bounded. Finally, the results of simulation example further verify the validity of this decentralized output-feedback control scheme.

An adaptive decentralized output-feedback control problem is investigated for a class of pure-feedback large-scale nonlinear systems with mismatched uncertainties, unknown dead-zones and unknown virtual control coefficients. At the same time, the nonlinear interconnections involve time-varying delays. Because only output information can be obtained, a state observer is constructed first. By using the infinite approximation ability of the radial basis function neural networks, the difficulty caused by the unknown nonlinearities is successfully overcome. Based on the appropriate Lyapunov–Krasovskii functions, the time-delay terms are compensated. The unknown virtual control coefficients are disposed by the convex combination method. By combining the backstepping technique with decentralized control principle, the adaptive neural decentralized output-feedback controllers are constructed to guarantee all the signals of the resulting closed-loop systems are bounded. And meanwhile, the error signals can converge to a small neighborhood of the origin. The simulation examples are provided to test our results.

This paper studies the problem of the secure state estimation of cyber-physical systems. The system model we studied is a class of discrete-time systems with state delay and sparse sensor attacks. In the design of the observer, a Projection Operator is utilized to determine the correct attack set, and the gain matrix will be switched accordingly. In this way, the excessive estimation error could be avoided effectively. In addition, based on the generalization of the classical Krasovskii Stability Theorem for stability analysis of time-delay systems, a Lyapunov-Krasovskii functional is chosen and a sufficient condition for the existence of the observer together with its design method is determined. The designed observer overcomes the difficulties caused by state delay and sensor attacks, and has good performance in secure estimation. Finally, two examples are given to verify that the observer can restore the desired estimate in a short time when a sudden attack occurs.

This paper focuses on the finite-time consensus tracking control problem of nonlinear multi-agent systems. Dynamics of each agent has completely unknown nonlinear terms that cannot be directly used...

This paper investigates the design problem of fuzzy dynamic output feedback $H_\infty $ controller for nonlinear networked systems via mismatched membership functions and adaptive event-triggered (AET) mechanism. Firstly, an AET mechanism is introduced to save communication resources, which causes the controller and the original system's premise variables to be asynchronous. Then, considering the influence of AET and mismatched membership functions, a model of fuzzy control system is established. In addition, utilizing the Lyapunov-Krasovskii(L-K) functional, sufficient conditions for the global exponential stability of the closed-loop system with $H_\infty $ performance are derived. Besides, the controller parameters and event-triggered (ET) weight matrix are solved by a set of linear matrix inequalities (LMIs). Finally, an example is given to demonstrate the effectiveness of the proposed control method.

This paper addresses neural adaptive quantized control for switched nonlinear non-strict feedback systems. The systems under consideration have unknown virtual control coefficients, and the system states are unmeasurable. Another feature of the systems is that they have quantized input and output signals. The control objective is first to set up a robust switched observer, and then an adaptive neural tracking control strategy is proposed via estimated state feedback. By Lyapunov stability theory, we show that the constructed adaptive neural controller guarantees a small tracking error and the boundedness of all the closed-loop signals, despite the fact that the systems contain unknown virtual control coefficients, and quantized input and output signals. Eventually, two examples are employed to demonstrate the validity of our results.

This research mainly addresses adaptive neural fast finite-time control of nonlinear strict-feedback multi-agent systems (MASs). Compared to the previous results on finite-time control of multi-agent systems, the nonlinearities in the system under consideration are completely unknown. Furthermore, radial basis function (RBF) neural networks (NNs) are adopted to model these nonlinear functions. In order to avoid the appearance of singularities during derivation, the design of the virtual control functions uses the form of piecewise functions. A novel criterion of fast finite-time stability is developed to solve the proposed control issue. Based on this criterion, a distributed adaptive fast finite-time tracking strategy is presented by combining neural network method and backstepping technique. It is proven that the proposed scheme is able to achieve consensus tracking in finite time. The errors rapidly tend to a small region around the origin, meanwhile other closed-loop signals are always bounded. The effectiveness of the developed control protocol is verified by a numerical simulation.

This paper investigates the problem of finite-time consensus tracking control for a class of 2-order nonlinear multi-agent systems (MASs). In order to present a consensus control protocol by adaptive neural control approach, a novel fast finite-time stability criterion is first set up, which provides a theoretical basis for applying approximation-based adaptive control approaches to solve the finite-time control issues. Furthermore, an adaptive neural fast finite-time consensus tracking controller is constructed based on the developed finite-time stability criterion. The suggested adaptive neural backstepping control design scheme successfully avoids the problem of singularity of controllers. Under the action of the presented protocol, the output of each follower tracks the reference signal and other signals of the closed-loop system remain bounded in finite time. The efficacy of the proposed control scheme is confirmed by simulation study.

In this paper, an observer-based adaptive neural network finite-time dynamic surface control method is proposed for the position tracking control of PMSM stochastic nonlinear systems with iron losses. First, the finite-time technology is used to realize the fast and effective tracking of the desired signal and make the system have better robust performance. Then, the adaptive neural network (NN) technology and state observer are applied to approximating the uncertain nonlinear functions and estimating the immeasurable states, respectively. And, the dynamic surface control (DSC) technology is used to resolve the “explosion of complexity” problem. In addition, the influence of iron losses and stochastic disturbances in the system is considered, and a quartic stochastic Lyapunov function is established to analyze the stability of the system. Finally, the simulation results show the effectiveness of the proposed method.

This paper studies the stabilization via observer-based feedback control for fractional-order systems with input delay. Firstly, the system is transformed into an input-delay-free system by using Smith predictor. Then a necessary and sufficient condition for observer-based controller design is presented, based on linear matrix inequalities (LMIs). While, implementation problem of the controller is provided. Finally, a numerical example and a fractional inverted pendulum system example are given to illustrate the effectiveness of the design method.

Focusing on the problem of position tracking control for permanent magnet synchronous motors (PMSMs) with full-state constraints, this article proposes an adaptive fuzzy control scheme based on command filtering error compensation mechanism. Firstly, the unknown nonlinear functions of PMSM drive systems are approximated by utilizing the fuzzy logic systems (FLSs). Then, the command filtering technique is employed to deal with the “explosion of complexity” problem arising from conventional backstepping scheme, and the filtering errors are reduced by the error compensation mechanism. In addition, the barrier Lyapunov functions (BLFs) are constructed to guarantee that the state variables are restricted in compact bounding sets. Finally, simulation results show the effectiveness of the proposed scheme.

In this article, an adaptive neural-network (NN) command-filtered output-feedback control strategy is proposed for a class of stochastic nonlinear systems (SNSs) with the actuator constraint. The problem of ``explosion of complexity'' existing in the conventional backstepping design procedure for SNSs is successfully resolved based on the command filter technique, and the error compensation mechanism is introduced to remove effectively the influence of filtered error. By using the NNs to identify the unknown nonlinear functions, a neural-network-based state observer is designed to estimate the unmeasurable states of the SNSs. Based on the quartic Lyapunov function, the stability of stochastic closed-loop systems is analyzed. It is proved that all signals of the closed-loop systems are bounded in probability, and the tracking error approaches a small neighborhood of the origin in probability. Finally, the effectiveness of the developed control algorithm in this article is verified by a comparison example.

This paper aims at the trajectory tracking of a quadrotor. A novel fixed-time backstepping control design scheme is proposed for the quadrotor based on adaptive neural control approach. The suggested adaptive controller ensures that the quadrotor well tracks the desired trajectory in finite time in spite of appearance of model uncertainties. Finally, simulation results are given to verify the effectiveness of the proposed control strategy.

This paper proposes a neural networks-based finite-time dynamic surface position tracking control method for induction motors with input saturation in electric vehicle drive systems. Firstly, the neural networks are utilized to approximate the unknown nonlinear functions and the dynamic surface control is used to solve the problem of “explosion of complexity” in traditional backstepping technology. Then, the finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the iron losses and input saturation are considered to improve control accuracy. At last, the results of simulation contrast experiments show that the proposed control method realizes ideal tracking effect considering iron losses and input saturation of the induction motors.

A discrete-time adaptive fuzzy control method is introduced to achieve the speed regulation for induction motors (IMs) with input saturation via command filtering in this paper. First, the continuous model of IMs drive system is transformed into discrete-time form by using Euler formula. Then, the fuzzy logic systems are used to approximate the unknown nonlinear functions in the discrete-time drive system. In addition, the command filtering control method is introduced to overcome the “explosion of complexity” problem in the design process of traditional backstepping method. It is verified that all the closed-loop signals are bounded and the outputs can track the given reference signals well. Finally, simulation results illustrate the validity of the discrete-time control method.

In this paper, an adaptive output feedback control via command filtered backstepping is proposed for a class of uncertain nonlinear systems with full-state constraints. Firstly, the “explosion of complexity” problem inherent in all the existing results of backstepping-based full-state constraints area is solved by the proposed control. Secondly, a state observer is designed to estimate the immeasurable states and the command filtered technology is utilized to cope with the problem in the present backstepping-based results of constrained nonlinear systems. Thirdly, the barrier Lyapunov functions are constructed to ensure the constraints are not transgressed. Then, an error compensating mechanism is developed to cope with filtering errors and only one adaptive law is needed for the full-state constrained nonlinear systems. An example is given to illustrate the validity and potential of the new design scheme.

This manuscript studies a finite-time tracking problem of switched stochastic nonlinear uncertain systems. By utilizing a comparison theorem and a mean value theorem of integrals, a significant finite-time stability criterion for stochastic nonlinear systems is first set up. Then, combining a common Lyapunov function method and an adaptive fuzzy control approach, a novel common control scheme is formed. Under the proposed adaptive mechanism, the system performance is achieved in finite-time. By using the universal approximation ability, the nonlinear functions and their bounding functions may be completely unknown to the designer, which is more in line with reality than the existing finite-time researches for stochastic nonlinear systems.

This paper is concerned with the regularization and stabilization problems for rectangular discrete-time fuzzy systems with time delay. A dynamic compensation is designed to ensure that the close-loop system is square, and a necessary and sufficient condition is proposed to guarantee the existence of a dynamic compensation with which the close-loop system is regular and causal. Moreover, sufficient conditions are derived in terms of bilinear matrix inequalities to guarantee the admissibility of the closed-loop system. We present an efficient algorithm which is proved to be convergent to solve the conditions. Two examples are given to show the effectiveness and efficiency of the proposed method.

This paper studies the position tracking control problem for permanent magnet synchronous motors (PMSMs) with parameter uncertainties. Firstly, the command filtered method is employed to overcome the “explosion of complexity” in traditional backstepping method. Then, in order to reduce the errors produced by command filters, error compensation mechanism is adopted. In addition, the finite-time control method makes the tracking error converge to the smaller neighborhood in the finite time. The adaptive fuzzy control is used to approximate the nonlinear functions. Finally, the simulation results proved the designed control method can overcome the influence of parameter uncertainties and achieve the satisfactory position tracking control.

This paper investigates the adaptive fuzzy output consensus tracking control for nonlinear multi-agent systems in the presence of input saturation. The interaction among the agents is described by a directed graph . Firstly, a local fuzzy state estimator is proposed to reconstruct the unmeasured state of each agent. Then, a novel command filtered backstepping based distributed adaptive control law is designed, where theunknown nonlinear dynamics are approximated by using the fuzzy logic system . The proposed control law can guarantee that the output consensus tracking errors converge into a sufficiently small neighborhood of the origin and all signals in the closed-loop system are bounded although the input saturation exists. Simulation results show the effectiveness of the proposed design.

This paper focuses on the stabilization problem for a class of rectangular descriptor systems through dynamic compensation. Such class of systems may not be stabilized by delay-free dynamic compensators, while delayed dynamic compensator could achieve such purpose. We provide a design scheme of time-delayed dynamic compensator which makes the closed-loop system admissible. The design involves solving a quadratic matrix inequality, and consequently, we build a linear matrix inequality (LMI) based algorithm to compute compensator gains. We verify that, under certain circumstances for which delay-free dynamic compensators fail to stabilize, the proposed method works well. An illustrative example demonstrates the usefulness of the present scheme.

In this paper, a novel asymmetric Lyapunov-Krasovskii functional (LKF) method for the stability of Takagi-Sugeno (T-S) fuzzy systems with time-varying delay is proposed. For further reducing conservatism, the method is combined with the improved membership-function-dependent technique. A numerical example is given to demonstrate the advantage of our method and stability criterion numerically.

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

In this paper, an event-triggered adaptive neural control issue is addressed for a class of switched unknown strict-feedback nonlinear system under constraint output. To deal with the unknown nonlinear system, the radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions. Under adaptive backstepping technique, associated with barrier Lyapunov function method, an event-triggered controller is designed to ensure that the system's output signal follows a given reference signal. meanwhile, the system output signal meets the asymmetric constraint requirement. The proposed control strategy is guaranteed to solve the presented problem. Finally, a simulation example is presented to demonstrate the efficacy of the proposed scheme.

The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.

This brief is concerned with the finite-time tracking control problem for switched nonlinear systems with arbitrary switching and hysteresis input. The neural networks are utilized to cope with the unknown nonlinear functions. To present the finite-time adaptive neural control strategy, a new criterion of practical finite-time stability is first developed. Compared with the traditional command filter technique, the main advantage is that the improved error compensation signals are designed to remove the filtered error and the Levant differentiators are introduced to approximate the derivative of the virtual control signal. The finite-time adaptive neural controller is proposed via the new command filter backstepping technique, and the tracking error converges to a small neighborhood of the origin in finite time. Finally, the simulation results are provided to testify the validity of the proposed method.

This paper considers the finite time state estimation problem of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time-varying delays. By resorting to the Lyapunov function approach, the Wirtinger inequality and the reciprocally convex approach, a delay-dependent criterion in terms of LMIs is established to guarantee the finite-time boundedness of the error-state system for the addressed system. Meanwhile, an effective state estimator is designed to estimate the network states through the available output measurements. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.

The adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging...

In this paper, an adaptive neural control issue is addressed for a class of switched unknown strict-feedback nonlinear system under constraint output, in which the input signal is quantized. The control goal is to design a quantized controller to ensure that the system's output signal follows a given reference signal, meanwhile, the system output signal meets the asymmetric constraint requirement. To this end, the radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions. Adaptive backstepping technique and barrier Lyapunov function method are utilized to design the tracking controller and analyze the closed-loop stability. The proposed control strategy is shown to deal with the presented problem well. Finally, two simulation examples are presented to illustrate the efficacy of the design scheme.

This paper is concerned with the Lagrange exponential stability problem of complex-valued bidirectional associative memory neural networks with time-varying delays. On the basis of activation functions satisfying different assumption conditions, by combining the Lyapunov function approach with some inequalities techniques, different sufficient criteria including algebraic conditions and the condition in terms of LMI are derived to guarantee Lagrange exponential stability of the addressed system, respectively. Moreover, the estimations of different globally attractive sets named the convergence balls are also provided. In the end, the effectiveness and superiority–inferiority of these different results are verified by illustrative examples.

This paper focuses on the stabilization problem for rectangular descriptor fractional order systems (FOSs) with $0