Indirect Adaptive Control of Nonlinearly Parameterized Nonlinear Dissipative Systems

TL;DR

This paper introduces a novel indirect adaptive control method for nonlinear dissipative systems with nonlinearly parameterized models, ensuring global parameter convergence and stability using a power-balance based estimator.

Contribution

It proposes a new parameter estimation technique based on the power-balance equation that guarantees exponential convergence under weak excitation conditions.

Findings

Ensures global, exponential parameter convergence.

Applicable to a large class of physical systems including passive systems.

Demonstrates effectiveness through illustrative examples.

Abstract

In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition -- this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the "power-balance" equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power-balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends -- possibly nonlinearly -- on the unknown plant parameters, and apply a certainty-equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.