1. Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems
- Author
-
Vlahakis, Eleftherios E., Lindemann, Lars, Sopasakis, Pantelis, and Dimarogonas, Dimos V.
- Subjects
Electrical Engineering and Systems Science - Systems and Control - Abstract
We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the $S$-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size., Comment: To appear in IEEE Control Systems Letters (L-CSS)
- Published
- 2024