Finite-Horizon H∞ State Estimation for Periodic Neural Networks Over Fading Channels

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.

Optimal Asynchronous Stabilization for Boolean Control Networks With Lebesgue Sampling

Using semitensor products (STPs) of matrices, sampled-data state-feedback control (SDSFC) with the Lebesgue sampling region S_τ is first considered to stabilize a Boolean control network (BCN) to a fixed point, under which a necessary and sufficient condition for stabilization is obtained when the considered BCN with the Lebesgue sampling region is converted to a switching system. Meanwhile, the corresponding asynchronous SDSFC gains are designed from a sequence of reachable sets. Then, an algorithm is shown to obtain the minimal number of controlling times and all states globally stabilize to the desired state with the fastest convergence rate under the minimal number of controlling times. Besides, the results have been extended to p Lebesgue sampling regions S_τi, i=1,2,…, p . And some results are presented for this situation, including the necessary and sufficient conditions stabilization under the p Lebesgue sampling regions, the asynchronous SDSFC gains, and the algorithm to obtain the optimal states sampling regions. Examples are listed to show the effectiveness of our results, and the biological example indicates that the SDSFC with Lebesgue sampling is also suitable for stochastic BCNs.

Adaptive Bipartite Tracking Control of Nonlinear Multiagent Systems With Input Quantization

This article studies the bipartite tracking control problem of distributed nonlinear multiagent systems with input quantization, external disturbances, and actuator faults. We use the radial basis function (RBF) neural networks (NNs) to model unknown nonlinearities. Due to the fact that the upper bounds of disturbances and the number of actuator faults are unknown, an intermediate control law is designed based on a backstepping strategy, where a compensation term is introduced to eliminate external disturbances and actuator faults. Meanwhile, a novel smooth function is incorporated into the real distributed controller to reduce the effect of quantization on the virtual controller. The proposed distributed controller not only realizes the bipartite tracking control but also ensures that all signals are bounded in the closed-loop systems and the outputs of all followers converge to a neighborhood of the leader output. Finally, simulation results demonstrate the effectiveness of the proposed control algorithm.

Filtering for Discrete-Time Takagi-Sugeno Fuzzy Nonhomogeneous Markov Jump Systems With Quantization Effects

This article deals with the problem of H_∞ and l₂-l_∞ filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, respectively. The time-varying transition probabilities are in a polytope set. To reduce conservativeness, a mode-dependent logarithmic quantizer is considered in this article. Based on the fuzzy-rule-dependent Lyapunov function, sufficient conditions are given such that the filtering error system is stochastically stable and has a prescribed H_∞ or l₂-l_∞ performance index, respectively. Finally, a practical example is provided to illustrate the effectiveness of the proposed fuzzy filter design methods.

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.

Gain-Scheduled Finite-Time Synchronization for Reaction-Diffusion Memristive Neural Networks Subject to Inconsistent Markov Chains

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.

Learning Tracking Control Over Unknown Fading Channels Without System Information

A novel data-driven learning control scheme is proposed for unknown systems with unknown fading sensor channels. The fading randomness is modeled by multiplicative and additive random variables subject to certain unknown distributions. In this scheme, we propose an error transmission mode and an iterative gradient estimation method. Unlike the conventional transmission mode where the output is directly transmitted back to the controller, in the error transmission mode, we send the desired reference to the plant such that tracking errors can be calculated locally and then transmitted back through the fading channel. Using the faded tracking error data only, the gradient for updating input is iteratively estimated by a random difference technique along the iteration axis. This gradient acts as the updating term of the control signal; therefore, information on the system and the fading channel is no longer required. The proposed scheme is proved effective in tracking the desired reference under random fading communication environments. Theoretical results are verified by simulations.

Neural-Network-Based Event-Triggered Adaptive Control of Nonaffine Nonlinear Multiagent Systems With Dynamic Uncertainties

This article addresses the adaptive event-triggered neural control problem for nonaffine pure-feedback nonlinear multiagent systems with dynamic disturbance, unmodeled dynamics, and dead-zone input. Radial basis function neural networks are applied to approximate the unknown nonlinear function. A dynamic signal is constructed to deal with the design difficulties in the unmodeled dynamics. Moreover, to reduce the communication burden, we propose an event-triggered strategy with a varying threshold. Based on the Lyapunov function method and adaptive neural control approach, a novel event-triggered control protocol is constructed, which realizes that the outputs of all followers converge to a neighborhood of the leader's output and ensures that all signals are bounded in the closed-loop system. An illustrative simulation example is applied to verify the usefulness of the proposed algorithms.

Relaxed Stability Criteria for Neural Networks With Time-Varying Delay Using Extended Secondary Delay Partitioning and Equivalent Reciprocal Convex Combination Techniques

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.

Distributed Sliding-Mode Tracking Control of Second-Order Nonlinear Multiagent Systems: An Event-Triggered Approach

The event-triggered tracking control problem of second-order multiagent systems in consideration of system nonlinearities is investigated by utilizing the distributed sliding-mode control (SMC) approach. An event-triggered strategy is proposed to decrease the controller sampling frequency and save the network communication resources; the triggering condition is then established for leader-following multiagent systems. In this article, by utilizing the distributed event-based sliding-mode controller, the system state of second-order multiagent systems with system nonlinearities is capable of approaching the integral sliding-mode surface in finite time. A novel integral sliding-mode surface is constructed in this article to guarantee the consensus tracking performance in the existence of system nonlinearities as the state trajectories of second-order integrator systems move on the constructed sliding manifold. By employing the Lyapunov approach, sufficient conditions are deduced to ensure that the consensus tracking performance is obtained for the closed-loop system. Furthermore, it is presented that the triggering scheme can effectively reduce state updates and eliminate the Zeno behavior. A simulation example is provided to testify the validity of our proposed methodology.