Online Optimal Control with Affine Constraints

10/10/2020 ∙ by Yingying Li, et al. ∙ 0

This paper considers online optimal control with affine constraints on the states and actions under linear dynamics with random disturbances. We consider convex stage cost functions that change adversarially. Besides, we consider time-invariant and known system dynamics and constraints. To solve this problem, we propose Online Gradient Descent with Buffer Zone (OGD-BZ). Theoretically, we show that OGD-BZ can guarantee the system to satisfy all the constraints despite any realization of the disturbances under proper parameters. Further, we investigate the policy regret of OGD-BZ, which compares OGD-BZ's performance with the performance of the optimal linear policy in hindsight. We show that OGD-BZ can achieve Õ(√(T)) policy regret under proper parameters, where Õ(·) absorbs logarithmic terms of T.

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