Jump Law of Co-State in Optimal Control for State-Dependent Switched Systems and Applications

TL;DR

This paper derives a jump law for co-states in optimal control of state-dependent switched systems, providing a new theoretical framework and an efficient algorithm validated by simulations.

Contribution

It introduces a novel jump law for co-states and an algorithm for optimal control in state-dependent hybrid systems, advancing existing methods.

Findings

The jump law is rigorously derived and validated by simulations.

The proposed algorithm outperforms existing methods in efficiency.

Numerical results demonstrate improved solution accuracy and computational speed.

Abstract

This paper presents the jump law of co-states in optimal control for state-dependent switched systems. The number of switches and the switching modes are assumed to be known a priori. A proposed jump law is rigorously derived by theoretical analysis and illustrated by simulation results. An algorithm is then proposed to solve optimal control for state-dependent hybrid systems. Through numerical simulations, we further show that the proposed approach is more efficient than existing methods in solving optimal control for state-dependent switched systems.