Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior

TL;DR

This paper presents an adaptive control method for discrete-time systems with unknown parameters, achieving linear-like behavior, bounded gain, and asymptotic set-point tracking under certain conditions.

Contribution

It introduces a pole-placement-based adaptive control law that guarantees linear-like closed-loop behavior and bounded gain for systems with uncertain parameters.

Findings

Proves exponential decay of system response from initial conditions.

Establishes a linear-like convolution bound with respect to inputs.

Demonstrates asymptotic tracking for constant disturbances.

Abstract

In this paper, we consider the problem of set-point tracking for a discrete-time plant with unknown plant parameters belonging to a convex and compact uncertainty set. We carry out parameter estimation for an associated auxiliary plant, and a pole-placement-based control law is employed. We prove that this adaptive controller provides desirable linear-like closed-loop behavior which guarantees a bound consisting of: exponential decay with respect to the initial condition, a linear-like convolution bound with respect to the exogenous inputs, and a constant scaled by the square root of the constant in the denominator of the parameter estimator update law. This implies that the system has a bounded gain. Moreover, asymptotic tracking is also proven when the disturbance is constant.