Abstract
The robust control problem of a class of nonlinear systems subject to external disturbances, control gain uncertainty, and nonlinear uncertainties is investigated in this paper using a nonlinearity estimator-based control approach. Different from the existing results, the crucial but highly restrictive hypothesis on the boundedness of nonlinear uncertainties is removed from this paper by means of the tools of semiglobal stabilization. By delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful level sets, the rigorous qualitative robustness performance is presented for the closed-loop system. Finally, an example of a single-link manipulator is utilized to demonstrate the performance specification claimed by the theoretical analysis.
Highlights
A fundamental and crucial task of control systems is to deal with external disturbances and uncertainties [1], [2], [3]
As an alternative approach to traditional robust control, various disturbance/uncertainty estimation and attenuation (DUEA) approaches have been proposed for disturbance rejection and uncertainty attenuation [6], [7], [8], [9], [10], [11]
The objective of this paper is to develop a nonlinearity estimator-based control approach for nonlinear system (2) such that the equilibrium of the closed-loop system is semi-globally stable even in the presence of nonlinear uncertainties and external disturbances
Summary
A fundamental and crucial task of control systems is to deal with external disturbances and uncertainties [1], [2], [3]. The traditional robust control using high control gains is recognized as a major design tool to suppress disturbances/uncertainties in nonlinear control theory [4]. Robust control is mostly achieved at a price of sacrificing the nominal control performance since the control performance in the nominal case is usually not directly taken into account [15]. Such a design philosophy may cause unsatisfactory overall performance since most practical systems usually operate around their nominal operation point, and rarely operate far away from their nominal operation point [5]. In the absence of disturbances/uncertainties, the patch estimator would be inactivated
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