Global practical tracking by output feedback for nonlinear systems with unknown growth rate and time delay.

Xuehua Yan,Xinmin Song

doi:10.1155/2014/713081

Abstract

This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results.

Highlights

As well known that the presence of time delay has a significant effect on system performance, it often causes deterioration of control system performance and may induce instability, oscillation, and poor performance in a large number of important physical, industrial, and engineering problems involving [1] networked control systems, information, or energy transportation
Control design methods for time delay systems can be classified into two categories: delay-dependent [2,3,4, 11] and delay-independent [5,6,7,8,9,10]
We are concerned with the practical tracking for a more general class of uncertain nonlinear systems in the following form

Summary

Introduction

As well known that the presence of time delay has a significant effect on system performance, it often causes deterioration of control system performance and may induce instability, oscillation, and poor performance in a large number of important physical, industrial, and engineering problems involving [1] networked control systems, information, or energy transportation. The objective of the paper is to design an adaptive controller such that the resulting closed-loop system is welldefined and globally bounded on R+, and for any prescribed tracking precision l > 0 and every initial condition, there is a finite time Tλ > 0 such that supt≥Tλ |y(t)| = supt≥Tλ |η1(t)−yr(t)| ≤ l (as described in [20]). To make this possible, the following assumptions are imposed on system (1) and reference signal yr. [20] studies global practical tracking problem by output feedback, it does not include the time delay

Global Practical Tracking Control via Output Feedback

An Illustrative Example

Conclusions

The Proof of Proposition 5

The Proof of Proposition 6