Sliding mode control for uncertain fractional-order reaction-diffusion memristor neural networks with time delays.

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction-diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction-diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

Predefined-Time Output-Feedback Leader-Following Consensus of Pure-Feedback Multiagent Systems.

This article delves into the predefined-time output-feedback leader-following consensus problem of uncertain pure-feedback nonlinear multiagent systems for the first time. To streamline subsequent design, the original systems in pure-feedback form are first transformed into canonical systems. Following this, a distributed predefined-time extended state observer (ESO) and a local predefined-time ESO are developed to reconstruct the unknown states/lumped disturbance of the transformed leader system and follower systems, respectively. Based on the estimated states and utilizing a bounded regulation function, two nonsingular and nonconservative predefined-time control laws are formulated to achieve consensus tracking. The proposed method showcases the following advantages: 1) the actual convergence time rather than the upper bound of the convergence time (UBCT) of the tracking errors can be explicitly specified a priori regardless of the initial conditions in a bounded region, optimizing control energy usage and 2) the system overshoot could be effectively reduced by selecting appropriate parameters for the regulation function. Finally, numerical examples are conducted to verify the obtained results.

Projective Synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme.

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.

Global Stability of Fractional Nonlinear Differential Systems With State-Dependent Delayed Impulses.

The fractional-order (FO) nonlinear differential system with state-dependent (SD) delayed impulses (DI) is considered in this brief. The considered impulses are related to the delayed state of the system and the delays are SD. A novel lemma for the monotonicity of the solution of Caputo's FO derivative equation is given. By means of linear matrix inequality (LMI) and several comparative arguments, criteria of uniform stability, uniform asymptotical stability, and Mittag-Leffler stability are obtained. Compared with other works on integer-order (IO) impulsive delayed systems with SD delays or fixed delays, how to impose constraints on parameters and impulses is explored, without imposing the boundedness on the state delays. Two examples are implemented to examine the practicality and sharpness of our theoretical analysis.

Synchronization of uncertain general fractional unified chaotic systems via finite-time adaptive sliding mode control.

This paper employs two adaptive sliding mode control (ASMC) strategies to accomplish finite-time synchronization of uncertain general fractional unified chaotic systems (UGFUCSs) when uncertainty and external disturbance exist. First, general fractional unified chaotic system (GFUCS) is developed. GFUCS may be transitioned from general Lorenz system to general Chen system, and the general kernel function could compress and extend the time domain. Furthermore, two ASMC methods are applied to finite-time synchronization of UGFUCSs, where system states arrive at sliding surfaces in finite-time. The first ASMC approach utilizes three sliding mode controllers to achieve synchronization between chaotic systems, while the second ASMC method needs just one sliding mode controller to produce synchronization between chaotic systems. Finally, the effectiveness of the proposed ASMC approaches is verified using numerical simulations.

A fixed-time distributed extended state observer for uncertain second-order nonlinear system.

This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer.

Finite-Time Observer-Based Sliding-Mode Control for Markovian Jump Systems With Switching Chain: Average Dwell-Time Method.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

Fuzzy event-triggered tracking control for nonlinear unreliable networked systems.

This article addresses a fuzzy event-triggered tracking control problem of unreliable networked systems. An event-based tracking controller is put forward to control the plant in fuzzy form. The looped Lyapunov-Krasovskii functional method is made use of conducting stability analysis, and sufficient conditions on the controller are determined. As a result, the tracking control performance is achieved for the controlled system. The feasibility of the presented tracking control design is verified by some examples.

Global Mittag-Leffler synchronization of coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks via sliding mode control.

This paper studies the sliding mode control method for coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks on a directed non-strongly connected topology. A novel fractional integral sliding mode surface and the corresponding control law are designed to realize global Mittag-Leffler synchronization. The sufficient conditions for synchronization and reachability of the sliding mode surface are derived via the hierarchical method and the Lyapunov method. Finally, simulations are provided to verify our theoretical findings.

Impact of fear effect and prey refuge on a fractional order prey-predator system with Beddington-DeAngelis functional response.

In this article, a fractional-order prey-predator system with Beddington-DeAngelis functional response incorporating two significant factors, namely, dread of predators and prey shelter are proposed and studied. Because the life cycle of prey species is memory, the fractional calculus equation is considered to study the dynamic behavior of the proposed system. The sufficient conditions to ensure the existence and uniqueness of the system solution are found, and the legitimacy and well posedness in the biological sense of the system solution, such as nonnegativity and boundedness, are proved. The stability of all equilibrium points of the system is analyzed by an eigenvalue analysis method, and it is proved that the system generates Hopf bifurcation nearby the coexistence equilibrium with regard to three parameters: the fear coefficient k, the rate of prey shelters p, and the order of fractional derivative q. Compared with the integer derivative, the system dynamics in the situation of fractional derivative is more stable. We observe an interesting phenomenon through the simulation: with the increase in the level of the fear effect, the stability of the positive equilibrium point changes from stable to unstable and then to stable. At this time, there are two Hopf branches nearby the positive equilibrium point with respect to the fear coefficient k, and the system can be in a stable state at very low or high level of the fear effect. In addition, when the order of the fractional differential equation of the system decreases continuously, the stability of the system will change from unstable to stable, especially in the case of low-level fear caused by predators and low rate of prey shelters. Therefore, our findings support the view that the strong memory can promote the stable coexistence of two species in the prey-predator system, while fading memory of species will worsen the stable coexistence of two species in the proposed system.

Uniform Stability of Complex-Valued Neural Networks of Fractional Order With Linear Impulses and Fixed Time Delays.

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

Global Mittag-Leffler Stability of the Delayed Fractional-Coupled Reaction-Diffusion System on Networks Without Strong Connectedness.

In this article, we mainly consider the existence of solutions and global Mittag-Leffler stability of delayed fractional-order coupled reaction-diffusion neural networks without strong connectedness. Using the Leary-Schauder's fixed point theorem and the Lyapunov method, some criteria for the existence of solutions and global Mittag-Leffler stability are given. Finally, the correctness of the theory is verified by a numerical example.

Global Mittag-Leffler stability and existence of the solution for fractional-order complex-valued NNs with asynchronous time delays.

This paper is dedicated to exploring the global Mittag-Leffler stability of fractional-order complex-valued (CV) neural networks (NNs) with asynchronous time delays, which generates exponential stability of integer-order (IO) CVNNs. Here, asynchronous time delays mean that there are different time delays in different nodes. Two new inequalities concerning the product of two Mittag-Leffler functions and one novel lemma on a fractional derivative of the product of two functions are given with a rigorous theoretical proof. By utilizing three norms, several novel conditions are concluded to guarantee the global Mittag-Leffler stability and the existence and uniqueness of an equilibrium point. Considering the symbols of the matrix elements, the properties of an M-matrix are extended to the general cases, which introduces the excitatory and inhibitory impacts on neurons. Compared with IOCVNNs, exponential stability is the special case of our results, which means that our model and results are general. At last, two numerical experiments are carried out to explain the theoretical analysis.

Mittag-Leffler Synchronization of Delayed Fractional Memristor Neural Networks via Adaptive Control.

This brief is devoted to exploring the global Mittag-Leffler (ML) synchronization problem of fractional-order memristor neural networks (FOMNNs) with leakage delay via a hybrid adaptive controller. By applying Fillipov's theory and the Lyapunov functional method, the novel algebraic sufficient condition for the global ML synchronization of FOMNNs is derived. Finally, a simulation example is presented to show the practicability of our findings.

Decentralized Adaptive Command Filtered Neural Tracking Control of Large-Scale Nonlinear Systems: An Almost Fast Finite-Time Framework.

In this article, a decentralized adaptive finite-time tracking control scheme is proposed for a class of nonstrict feedback large-scale nonlinear interconnected systems with disturbances. First, a practical almost fast finite-time stability framework is established for a general nonlinear system, which is then applied to the design of the large-scale system under consideration. By fusing command filter technique and adaptive neural control and introducing two smooth functions, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented, while the obstacles caused by unknown interconnections are overcome. Moreover, according to the framework of practical almost fast finite-time stability, it is shown that all the closed-loop signals of the large-scale system are almost fast finite-time bounded, and the tracking errors can converge to arbitrarily small residual sets predefined in an almost fast finite time. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed finite-time decentralized control scheme.

Adaptive Control of Nonlinear Semi-Markovian Jump T-S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer.

The issue of observer-based adaptive sliding mode control of nonlinear Takagi-Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an H∞ performance disturbance attenuation level γ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

H∞ sliding mode control of discrete switched systems with time-varying delays.

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.

Robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays via sliding mode approach.

In this paper, the issue of robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays is investigated via sliding mode control (SMC). A sliding mode strategy is presented combined with the observer technique, since the system states are unmeasured. The distinguishing feature of the provided strategy is that a novel sliding surface is constructed based upon the estimated states such that the resulting full-order closed-loop system is generated. Furthermore, by employing Lyapunov-Krasovskii functional, new sufficient criteria in terms of a solvable linear matrix inequality (LMI) is derived, insuring that the closed-loop system is admissible with an H∞-norm bound. With the solution of the LMI, a corresponding sliding mode controller is obtained for reaching motion and reducing the chattering. At last, the theoretical results are verified in numerical tests.

Robust passive control for a class of uncertain neutral systems based on sliding mode observer.

The passivity-based sliding mode control (SMC) problem for a class of uncertain neutral systems with unmeasured states is investigated. Firstly, a particular non-fragile state observer is designed to generate the estimations of the system states, based upon which a novel integral-type sliding surface function is established for the control process. Secondly, a new sufficient condition for robust asymptotic stability and passivity of the resultant sliding mode dynamics (SMDs) is obtained in terms of linear matrix inequalities (LMIs). Thirdly, the finite-time reachability of the predesigned sliding surface is ensured by resorting to a novel adaptive SMC law. Finally, the validity and superiority of the scheme are justified via several examples.

Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability.

The problem of global exponential stability in mean square of delayed Markovian jump fuzzy cellular neural networks (DMJFCNNs) with generally uncertain transition rates (GUTRs) is investigated in this paper. In this GUTR neural network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than the existing ones. By constructing suitable Lyapunov functionals, several sufficient conditions on the exponential stability in mean square of its equilibrium solution are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and efficiency of our results.