Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints

• URL: http://arxiv.org/abs/2304.00569v1
• Date: Sun, 2 Apr 2023 16:38:13 GMT
• Title: Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints
• Authors: Seth Siriya, Jingge Zhu, Dragan Ne\v{s}i\'c, Ye Pu
• Abstract summary: We consider the problem of adaptive stabilization for discrete-time, multi-dimensional systems with bounded control input constraints and unbounded disturbances. We propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control.
• Score: 3.8004168340068336
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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