Switched Optimal Control with Dwell Time Constraints

TL;DR

This paper introduces a novel embedding-based method for solving switched optimal control problems with dwell time constraints by combining a modified embedded optimal control problem with a filtering technique to ensure feasibility.

Contribution

It proposes a new approach that integrates a filter layer with a modified embedded optimal control problem to handle dwell time constraints in switched control systems.

Findings

The method effectively enforces dwell time constraints.

It produces feasible solutions for switched optimal control problems.

The approach maintains near-optimal performance despite filtering.

Abstract

This paper presents an embedding-based approach for solving switched optimal control problems (SOCPs) with dwell time constraints. At first, an embedded optimal control problem (EOCP) is defined by replacing the discrete switching signal with a continuous embedded variable that can take intermediate values between the discrete modes. While embedding enables solutions of SOCPs via conventional techniques, optimal solutions of EOCPs often involve nonexistent modes and thus may not be feasible for the SOCP. In the modified EOCP (MEOCP), a concave function is added to the cost function to enforce a bang-bang solution in the embedded variable, which results in feasible solutions for the SOCP. However, the MEOCP cannot guarantee the satisfaction of dwell-time constraints. In this paper, a MEOCP is combined with a filter layer to remove switching times that violate the dwell time constraint. Insertion gradients are used to minimize the effect of the filter on the optimal cost.