Huai-Ning Wu

New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi and Sugeno (T-S) fuzzy systems with a time-varying delay. A new method for the delay-dependent stability analysis and stabilization is suggested, which is less conservative than other existing ones. First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the open-loop fuzzy systems. In the derivation process, some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation, and among the terms in the Leibniz-Newton formula. Then, a delay-dependent stabilization condition based on the so-called parallel distributed compensation (PDC) scheme is worked out for the closed-loop fuzzy systems. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities (LMIs) and compared with the existing ones via two examples. Finally, application to control of a truck-trailer is also given to illustrate the effectiveness of the proposed design method.

Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control

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 is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

Passivity-based synchronization of a class of complex dynamical networks with time-varying delay

This paper proposes a complex delayed dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. By utilizing some inequality techniques, a sufficient condition ensuring the output strict passivity is derived for the proposed network model. Then, we reveal the relationship between output strict passivity and synchronization of the proposed network model. Moreover, based on the obtained passivity result and the relationship between output strict passivity and synchronization, a criterion for synchronization is established. Finally, a numerical example is provided to illustrate the correctness and effectiveness of the proposed results.

Off-Policy Reinforcement Learning for

The H∞ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear H∞ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that is generally impossible to be solved analytically. Even worse, model-based approaches cannot be used for approximately solving HJI equation, when the accurate system model is unavailable or costly to obtain in practice. To overcome these difficulties, an off-policy reinforcement leaning (RL) method is introduced to learn the solution of HJI equation from real system data instead of mathematical system model, and its convergence is proved. In the off-policy RL method, the system data can be generated with arbitrary policies rather than the evaluating policy, which is extremely important and promising for practical systems. For implementation purpose, a neural network (NN)-based actor-critic structure is employed and a least-square NN weight update algorithm is derived based on the method of weighted residuals. Finally, the developed NN-based off-policy RL method is tested on a linear F16 aircraft plant, and further applied to a rotational/translational actuator system.

H_\infty

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newtons method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Control Design

An Hinfin fuzzy observer-based control design is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems with control constraints, for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. In the proposed control scheme, Galerkins method is initially applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T-S fuzzy model, a fuzzy observer-based controller is developed to stabilize the nonlinear PDE system and achieve an optimized Hinfin disturbance attenuation performance for the finite-dimensional slow system, while control constraints are respected. The outcome of the Hinfin fuzzy observer-based control problem is formulated as a bilinear matrix inequality (BMI) optimization problem. A local optimization algorithm that treats the BMI as a double linear matrix inequality is presented to solve this BMI optimization problem. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness.

Neural Network Based Online Simultaneous Policy Update Algorithm for Solving the HJI Equation in Nonlinear

This paper deals with the reliable linear quadratic (LQ) fuzzy control problem for continuous-time nonlinear systems with actuator faults. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear system. By using multiple Lyapunov functions, an improved linear matrix inequality (LMI) method for the design of reliable LQ fuzzy controllers is investigated, which reduces the conservatism of using a single Lyapunov function. The different upper bounds on the LQ performance cost function for the normal and different actuator fault cases are provided. A suboptimal reliable LQ fuzzy controller is given by means of an LMI optimization procedure, which can not only guarantee the stability of the closed-loop overall fuzzy system for all cases, but also provide an optimized upper bound on a weighted average LQ performance cost function. Finally, numerical simulations on the chaotic Lorenz system are given to illustrate the application of the proposed design method.

H_{\infty}

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H∞ synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H∞ synchronization. Some criteria for synchronization and H∞ synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.

Control

Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

H

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.