Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraints

TL;DR

This paper introduces an adaptive control scheme for stochastic linear systems with input constraints, ensuring mean square boundedness without prior parameter bounds, demonstrated through numerical examples.

Contribution

It develops a certainty-equivalence adaptive control method for scalar systems with unknown parameters and input bounds, guaranteeing stability under stochastic disturbances.

Findings

Mean square boundedness of system states is proven.

The control scheme does not require prior parameter bounds.

Numerical examples validate the theoretical results.

Abstract

We propose a certainty-equivalence scheme for adaptive control of scalar linear systems subject to additive, i.i.d. Gaussian disturbances and bounded control input constraints, without requiring prior knowledge of the bounds of the system parameters, nor the control direction. Assuming that the system is at-worst marginally stable, mean square boundedness of the closed-loop system states is proven. Lastly, numerical examples are presented to illustrate our results.