The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control design problem is considered for nonlinear systems with unknown internal system model. It known that the can be transformed into solving so-called Hamilton-Jacobi-Isaacs (HJI) equation, which a partial differential equation generally impossible to solved analytically. Even worse, model-based approaches cannot used approximately HJI when accurate model unavailable or costly...

Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, nodes through their states. second spatial diffusion terms. For former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. addition, considering theoretical coupling strength required for synchronization may be much larger than needed value, propose an adaptive strategy...

This paper proposes a directed complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. Based on the Lyapunov functional method pinning control technique, some sufficient conditions are obtained to guarantee synchronization proposed model. In addition, an adaptive strategy is obtain appropriate coupling strength for achieving synchronization. Furthermore, problem also investigated in this paper, general criterion ensuring...

In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using time-dependent Lyapunov functional. The advantage the new method that functional continuous at sampling times but not necessarily positive definite inside intervals. Compared with existing works, constructed makes full use information on piecewise constant input and actual pattern. terms parameterized linear matrix inequality (LMI) technique, less conservative stabilization condition...

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm developed to design an controller method. By using offline online data rather than the mathematical system model, PGADP improves with descent scheme. convergence proved by demonstrating that constructed Q -function sequence converges -function. Based on algorithm, method actor-critic structure weighted...

This paper studies the problem of event-triggered optimal control (ETOC) for continuous-time nonlinear systems and proposes a novel event-triggering condition that enables designing ETOC methods directly based on solution Hamilton-Jacobi-Bellman (HJB) equation. We provide formal performance guarantees by proving predetermined upper bound. Moreover, we also prove existence lower bound interexecution time. For implementation purposes, an adaptive dynamic programming (ADP) method is developed...

This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model employed to represent system norm-bounded parameter uncertainties parameters. aim design mode-independent controller such that closed-loop (MJFS) robustly stochastically stable. Based on stochastic Lyapunov function, condition using derived for MJFS in terms linear matrix...

This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi Sugeno (T-S) fuzzy systems a time-varying delay. A new method the suggested, which less conservative than other existing ones. First, based on Lyapunov-Krasovskii functional (LKF), criterion derived open-loop systems. In derivation process, some free weighting matrices are introduced to express relationships among terms of system equation, in Leibniz-Newton formula. Then,...

It is well known that the nonlinear H∞ state feedback control problem relies on solution of Hamilton-Jacobi-Isaacs (HJI) equation, which a partial differential equation has proven to be impossible solve analytically. In this paper, neural network (NN)-based online simultaneous policy update algorithm (SPUA) developed HJI in knowledge internal system dynamics not required. First, we propose an SPUA can viewed as reinforcement learning technique for two players learn their optimal actions...

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined inequality techniques, sufficient condition given to ensure that proposed network synchronized. addition, when external disturbances appear in network, criterion obtained guarantee H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This paper deals with the problem of fuzzy boundary control design for a class nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both measurement form and collocated considered. A Takagi–Sugeno (T–S) PDE model is first applied to accurately represent system. Based on T–S model, two types controllers, easily implemented since only actuators used, proposed ensure exponential stability resulting closed-loop Sufficient...

This paper considers a complex dynamical network model, in which the input and output vectors have different dimensions. We, respectively, investigate passivity relationship between strict synchronization of with fixed adaptive coupling strength. First, two new definitions are proposed, generalize some existing concepts passivity. By constructing appropriate Lyapunov functional, sufficient conditions ensuring passivity, derived for In addition, we also reveal employing synchronization,...

In this article, two kinds of leader-following formation control problems for second-order nonlinear multi-agent systems are investigated, that is, the cases with fixed topology and switching topology. For former, by constructing an appropriate Lyapunov functional utilising linear matrix inequality (LMI) method, we propose a algorithm which makes converge to desired formation. addition, is also developed coupled double-integrators constant reference velocity. Then extend these results case...

In this paper, we study a general array model of coupled reaction-diffusion neural networks (NNs) with adaptive coupling. order to ensure the passivity networks, some strategies tune coupling strengths among network nodes are designed. By utilizing inequality techniques and designed laws, several sufficient conditions ensuring obtained. addition, reveal relationship between synchronization NNs. Based on obtained results synchronization, global criterion is established. Finally, numerical...

Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider optimal control problem general highly SDPs, and propose an adaptive approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is compute empirical eigenfunctions (EEFs) SDP method snapshots. These EEFs together with singular perturbation technique then used...

In this paper, two types of linearly coupled neural networks with reaction-diffusion terms are proposed. We respectively investigate the adaptive synchronization these complex network models. With local information node dynamics, some novel strategies to tune coupling strengths among nodes designed. By constructing appropriate Lyapunov functionals and using inequality techniques, several sufficient conditions given for reaching by designed laws. Finally, examples numerical simulations...

Reinforcement learning has proved to be a powerful tool solve optimal control problems over the past few years. However, data-based constrained problem of nonaffine nonlinear discrete-time systems rarely been studied yet. To this problem, an adaptive approach is developed by using value iteration-based Q-learning (VIQL) with critic-only structure. Most existing methods require use certain performance index and only suit for linear or affine systems, which unreasonable in practice. overcome...

In this paper, two multiple weighted coupled reaction-diffusion neural networks (CRDNNs) with and without coupling delays are introduced. On the one hand, some finite-time passivity (FTP) concepts proposed for spatially temporally system different dimensions of output input. By choosing appropriate Lyapunov functionals controllers, several sufficient conditions presented to ensure FTP these CRDNNs. other synchronization (FTS) problem is also discussed CRDNNs delays, respectively. Finally,...

The data-driven H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method developed to learn the policy from real system data rather than mathematical model. First, Karhunen-Loève decomposition used compute empirical eigenfunctions, which are then employed derive a reduced-order model (ROM) slow subsystem based on singular...

A complex dynamical network consisting of N identical neural networks with reaction-diffusion terms is considered in this paper. First, several passivity definitions for the systems different dimensions input and output are given. By utilizing some inequality techniques, criteria presented, ensuring under designed adaptive law. Then, we discuss relationship between synchronization strict proposed model. Furthermore, these results extended to case when topological structure undirected....