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Asymptotic Tracking Control of SISO Nonlinear Systems With Unknown Time-Varying Coefficients: A Global Performance Guaranteed Solution | IEEE Journals & Magazine | IEEE Xplore

Asymptotic Tracking Control of SISO Nonlinear Systems With Unknown Time-Varying Coefficients: A Global Performance Guaranteed Solution


Abstract:

The particular interest of this article is mainly focusing on the prescribed performance control (PPC) problem for a class of single-input single-output (SISO) nonlinear ...Show More

Abstract:

The particular interest of this article is mainly focusing on the prescribed performance control (PPC) problem for a class of single-input single-output (SISO) nonlinear systems subject to serious mismatched uncertainties and unknown time-varying control coefficients. In contrast to most existing PPC works where the control coefficients are known or unknown while constant, the proposed control method allows multiple unknown and time-varying coefficients with nonidentical directions to be dealt with. The technical difficulty in the stability analysis arising from the multiple unknown and nonidentical directions is circumvented by proving that the effects of multiple Nussbaum-type gains in a single Lyapunov inequality can be quantified according to a newly established lemma (Lemma 2) regarding the enhanced Nussbaum functions. In addition, by resorting to a novel prescribed-time scaling function and an error transformation, it is proved that the current control method guarantees global prescribed performance in the sense that the output tracks the reference trajectory asymptotically with the tracking error converging into an arbitrarily predefined residual set at any rate of convergence within preset finite time irrespective of initial conditions and any design parameters, distinguishing itself from those semi-global results dependent on the initial conditions. The validity of the designed control scheme is confirmed by both theoretical analysis and numerical simulation.
Page(s): 3717 - 3727
Date of Publication: 18 March 2024

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I. Introduction

The transient and steady-state behavior of nonlinear systems is known as a significant performance indicator for the tracking control problem [1], [2], [3], [4]. A methodology called prescribed performance control (PPC) has been proposed in the pioneering works [5] and [6] where the comprehensive performance of the output tracking error is guaranteed upon using two decay boundary functions. Afterwards, much attention has been drawn to the tracking control problem with guaranteed performance, for instance [7], [8], [9], while the assumptions that, the involved system uncertain parameters are constant [7], [9] or the control coefficients are known [7], [8], are usually needed. It is imminently desired to develop an effective PPC algorithm for general nonlinear systems suffering from unknown time-varying parameters and control coefficients.

References

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