Differential stability of a class of convex optimal control problems
Duong Thi Viet An, Jen-Chih Yao, Nguyen Dong Yen
TL;DR
This paper investigates the stability of the optimal value function in a class of convex optimal control problems under initial state perturbations and noise, providing formulas for subdifferentials and illustrating their use.
Contribution
It introduces formulas for the subdifferential and singular subdifferential of the optimal value function in convex control problems with noise and perturbations.
Findings
Formulas for subdifferential computation are derived.
Procedures for calculating these subdifferentials are demonstrated.
Illustrative examples validate the theoretical results.
Abstract
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular subdifferential of the optimal value function at a given parameter are obtained by means of some recent results on differential stability in mathematical programming. The computation procedures and illustrative examples are presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.