An integral sliding-mode parallel control approach for general nonlinear systems via piecewise affine linear models

TL;DR

This paper introduces a novel integral sliding-mode parallel control method for stabilizing general nonlinear systems by approximating them with piecewise affine linear models, improving robustness and smoothness of control signals.

Contribution

It develops a new control approach using PALMs and sliding-mode control that relaxes input restrictions and handles uncertainties more effectively.

Findings

Successfully stabilizes nonlinear systems with the proposed method.

Produces smooth control signals around subspace boundaries.

Demonstrates effectiveness through numerical simulations.

Abstract

The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding-mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed scheme enjoys three favorable features: (i) some restrictions on the system input channel are eliminated, thus the developed method is more relaxed compared with the published approaches; (ii) it is convenient to be used to deal with both matched and unmatched uncertainties of the system; and (iii) the proposed piecewise parallel controller generates smooth control signals even around the boundaries between different subspaces, which makes the developed control strategy more implementable and reliable. Moreover, we provide discussions about the universality analysis of the developed control strategy for two kinds of typical nonlinear systems. Simulation results from two numerical examples further demonstrate the performance of the developed control approach.