Switched Optimal Control and Dwell Time Constraints: A Preliminary Study

TL;DR

This paper presents an embedding-based method for solving optimal control problems in switched systems with dwell-time constraints, effectively incorporating these constraints through an auxiliary cost and demonstrating its utility via simulations.

Contribution

Introduces a novel embedding-based approach that heuristically incorporates dwell-time constraints into optimal control problems with discrete and continuous variables.

Findings

Method successfully incorporates dwell-time constraints.

Simulations demonstrate improved control performance.

Auxiliary cost effectively enforces dwell-time constraints.

Abstract

Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching rate. This paper introduces an embedding-based-method to solve optimal control problems that have both discrete and continuous decision variables. Unlike existing methods, the developed technique can heuristically incorporate dwell-time constraints via an auxiliary cost, while also preserving other state and control constrains of the problem. Simulations results for a switched optimal control problem with and without the auxiliary cost showcase the utility of the developed method.