A Dynamic Programming-Inspired Approach for Mixed Integer Optimal Control Problems with Dwell Time Constraints

Abstract

This paper introduces a dynamic programming-inspired approach for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into this framework. The proposed method is tested on four MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that the proposed approach is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.

Keywords: Dynamic Programming, Optimal Control, Switched Systems