Adaptive Neural Output Feedback Control of Stochastic Nonlinear Systems with Unmodeled Dynamics

Xiaonan Xia,Tianping Zhang

doi:10.1155/2015/529862

Abstract

An adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states. The unmeasured states are estimated by K-filters, and unmodeled dynamics is dealt with by introducing a novel description based on Lyapunov function. The neural networks weight vector used to approximate the black box function is adjusted online. The unknown nonlinear system functions are handled together with some functions resulting from theoretical deduction, and such method effectively reduces the number of adaptive tuning parameters. Using dynamic surface control (DSC) technique, Itô formula, and Chebyshev’s inequality, the designed controller can guarantee that all the signals in the closed-loop system are bounded in probability, and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results are provided to verify the effectiveness of the proposed approach.

Highlights

During the past decades, backstepping in [1] and dynamic surface control (DSC) in [2] have become two most popular methods for adaptive controller design
In [26], by combining stochastic small-gain theorem with backstepping design technique, an adaptive output feedback control scheme was presented for a class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions
In this subsection, according to (21) and by using dynamic surface control method, we propose an output feedback stochastic adaptive tracking control scheme

Summary

Introduction

During the past decades, backstepping in [1] and dynamic surface control (DSC) in [2] have become two most popular methods for adaptive controller design. In [18], decentralized adaptive output-feedback control was designed based on high-gain K-filters and dynamic surface control method for a class of uncertain interconnected nonlinear systems. In [26], by combining stochastic small-gain theorem with backstepping design technique, an adaptive output feedback control scheme was presented for a class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions. Motivated by the above-mentioned results [4, 14, 32], in this paper, adaptive neural stochastic output feedback control is developed by combining K-filters with dynamic surface control to guarantee the stability of the closed-loop system. (i) Adaptive neural output feedback control is developed using K-filters and dynamic surface control for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states.

Problem Statement and Preliminaries

Adaptive Robust Controller Design and Stability Analysis

Simulation Results

Conclusions