Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints
This addresses the problem of stabilizing uncertain linear systems with constraints for control theory applications, but appears incremental as it builds on existing certainty-equivalent and saturation methods.
The paper tackles adaptive stabilization of discrete-time multi-dimensional linear systems with unknown parameters, input constraints, and stochastic disturbances by proposing a certainty-equivalent control scheme combining online parameter estimation with saturated linear control. It establishes a high probability stability bound for the closed-loop system under certain assumptions.
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To address this challenge, we propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Finally, numerical examples are presented to illustrate our results.