Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems

Abstract

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

“…For example, when p i , k ≡1, i =1,…, n , , system reduces to a standard strict‐feedback SSNS extensively studied in the literature. If , i =1,…, n , , system becomes into a high‐order SSNS was investigated in the work of Zhao et al If , i =1,…, n , , system changes into a SSNS investigated in the aforementioned works. () In the case, where p i , k ≡ p ( i =1,…, n , ) with p ∈(0,1), system becomes a special low‐order SSNS whose finite‐time stabilization problem was solved in the work of Huang and Xiang …”

“…For a class of strict‐feedback SSNSs with arbitrary switchings, the global stabilization by using state feedback was investigated in the work of Hou et al, as well as the adaptive output tracking control, was addressed in the work of Li et al In the work of Niu and Liu, a common state feedback controller was proposed for a class of high‐order SSNSs with identical powers. Subsequently, an adaptive control scheme was presented in the work of Zhao et al for solving the tracking problem of more general high‐order SSNSs by utilizing neural networks.…”

“…adaptive output tracking control, was addressed in the work of Li et al 28 In the work of Niu and Liu, 29 a common state feedback controller was proposed for a class of high-order SSNSs with identical powers. Subsequently, an adaptive control scheme was presented in the work of Zhao et al 30 for solving the tracking problem of more general high-order SSNSs by utilizing neural networks.…”

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

“…In the past decades, switched systems have become a research hot spot for its importance from one aspect that lots of industrial and physical systems, such as stirred tank reactor systems and single‐link manipulator systems, can be described as switched systems, which exhibits switching among subsystems relying on environmental factors. The existence of a common Lyapunov function is necessary for the whole subsystems if a switched system wants to keep stable under arbitrary switchings . Common Lyapunov function method was adopted in other works to realize stabilization or tracking of switched nonlinear systems.…”

Funnel‐like prescribed tracking control for uncertain nonlinear stochastic switched systems

“…In recent years, much effort has been made to deal with the stability and stabilization problems of switched systems, see other works and the references therein. By means of the universal function approximator, such as fuzzy logic systems (FLSs) or neural networks, the state feedback control problem of uncertain switched systems was studied in other works . Note that partial state information of many switched systems cannot be available for measurement in practice; some attempts have been devoted to solve the output feedback control problem for switched systems .…”