Exponentially Stable MRAC of MIMO Switched Systems with Matched Uncertainty and Completely Unknown Control Matrix

TL;DR

This paper develops an exponentially stable adaptive control method for MIMO switched systems with unknown control matrices and matched uncertainties, ensuring convergence and monotonicity despite switching signals.

Contribution

It introduces a novel MRAC approach applicable to systems with unknown switching signals and control matrices, extending existing adaptive control frameworks.

Findings

Ensures exponential convergence of errors within switching intervals.

Guarantees monotonicity of control parameters.

Validates effectiveness through numerical experiments.

Abstract

In this paper an attempt is made to extend the concept of the exponentially stable adaptive control to one class of multi-input-multi-output (MIMO) plants with matched nonlinearity and unknown piecewise constant parameters. Within the intervals between two consecutive parameter switches, the proposed adaptive control system ensures: 1) exponential convergence to zero of the parameter and reference model tracking errors, 2) the monotonicity of the control law adjustable parameters. Both properties are guaranteed in case the regressor is finitely exciting somewhere inside each of such intervals. Compared to the existing methods, the proposed one is applicable to systems with unknown switching signal function and completely unknown control matrix. The theoretical results are supported by the numerical experiments.