Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior
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.
Cite
@article{arxiv.2508.12225,
title = {Adaptive Control with Set-Point Tracking and Linear-like Closed-loop Behavior},
author = {Mohamad T. Shahab},
journal= {arXiv preprint arXiv:2508.12225},
year = {2025}
}
Comments
This is an extended version of a paper that will appear in the Proceedings of the 64th IEEE Conference on Decision and Control (CDC)