In this paper, an observer-based H _∞ sampled-data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems. With the aid of the modal decomposition technique, a nonlinear ordinary differential equation (ODE) model is initially derived to describe the dominant (slow) dynamics of the PDE system. Subsequently, the resulting nonlinear ODE model is accurately represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T- S fuzzy model, a finite-dimensional observer-based sampled-data fuzzy control design with H _∞ performance is developed for the PDE system via employing a novel time-dependent functional. The outcome of the observer-based H _∞ sampled-data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem. Moreover, an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal H _∞ sampled-data fuzzy controller. Finally, simulation results on the Fisher equation and a temperature cooling fin of high-speed aerospace vehicle illustrate that the proposed design method is effective.

In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.

Under spatially local averaged measurements (SLAMs), this article introduces a sampled-data fuzzy control (SDFC) for nonlinear delayed distributed parameter systems (DDPSs). Firstly, we use a Takagi-Sugeno (T-S) fuzzy parabolic partial differential-difference equation (PDdE) to accurately describe the nonlinear DDPS. Then, on basis of the obtained T-S fuzzy PDdE model, a SDFC design under SLAMs via spatial linear matrix inequalities (SLMIs) is subsequently developed to ensure the exponential stability of the closed-loop nonlinear DDPSs by using inequality techniques, and Lyapunov functional, where slow-varying and fast-varying delays are respected. Furthermore, to solve SLMIs, the SDFC design for nonlinear DDPSs under SLAMs is formulated as an LMI feasibility problem. Lastly, numerical simulations of an example are presented to support the given SDFC strategy.

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

This paper considers the estimator-based H∞ sampled-data fuzzy control (SDFC) problem of nonlinear parabolic partial differential equation (PDE) systems. First, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to represent the nonlinear PDE system. Second, with the aid of the T-S fuzzy PDE model, an estimator-based SDFC design ensuring the exponential stability of the closed-loop fuzzy PDE system with an H∞ performance is developed via a Lyapunov functional. The outcome of the estimator-based H∞ SDFC problem is formulated as a bilinear matrix inequality optimization problem, which is solved by an iterative algorithm on the basis of the linear matrix inequalities. Finally, for demonstrating the effectiveness of the proposed method, simulation results are provided to control the diffusion equation and the FitzHugh-Nagumo equation.