Global Practical Output Tracking of Inherently Nonlinear Systems Using Continuously Differentiable Controllers

Keylan Alimhan,Maksat N Kalimoldayev,Abilmazhin A Adamov,Naohisa Otsuka

doi:10.1155/2015/932097

Abstract

This paper considers the global practical output tracking problem by at least continuously differentiable (C1) state feedback for a class of uncertain nonlinear systems whose linearization around the origin may contain uncontrollable modes. Based on utilizing the homogeneous domination approach, we not only propose conditions of constructing a global continuously differentiable (C1) controller, but also provide explicit design schemes for such systems. Finally, a numerical example demonstrates the effectiveness of the result.

Highlights

The problem of global output tracking control of nonlinear systems is one of the most important and challenging problems in the field of nonlinear control
This paper considers the global practical output tracking problem by at least continuously differentiable (C1) state feedback for a class of uncertain nonlinear systems whose linearization around the origin may contain uncontrollable modes
The uncertain system (1) represents a general class of nonlinear systems considered in the nonlinear control literature

Summary

Introduction

The problem of global output tracking control of nonlinear systems is one of the most important and challenging problems in the field of nonlinear control. The problem of global practical output tracking control of the power integrator systems in form (1) has been studied extensively with various restrictions on the integrator powers and the additive functions fi(t, z, u)’s, which directly influence the availability of smooth or nonsmooth controllers; see [6,7,8,9,10]. In [8, 9], the practical output feedback tracking problem was investigated for a class of nonlinear systems with higherorder growing unmeasurable states, extending the results on stabilization in [11, 12]. The techniques from [11, 14] were recently extended in [10, 15] to the practical output tracking problem for nonlinear systems (1) by a continuous state feedback controller. The arguments of functions (or functionals) are sometimes omitted or simplified; for instance, we sometimes denote a function f(x(t)) by f(x), f(⋅), or f

Problem Statement and Preliminaries

Continuously Differentiable State Feedback Controller Design

An Illustrative Example

Conclusion