Numerical procedure for optimal control of hybrid systems with sliding modes, Part II

TL;DR

This paper presents a numerical method for solving hybrid optimal control problems with sliding modes, ensuring accurate tracking and convergence of adjoint equations, demonstrated through three practical control applications.

Contribution

It establishes the correspondence between discrete and continuous adjoint equations for systems with DAEs and demonstrates the method's effectiveness on real-world problems.

Findings

Discrete adjoint trajectories converge to continuous solutions

Method successfully applied to mechanical, medical, and automotive control problems

Ensures accurate tracking of sliding motion surfaces in hybrid systems

Abstract

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion surface. In the second part of the paper we demonstrate the correspondence between the discrete adjoint equations and the discretized version of the continuous adjoint equations in the case of system equations described by DAEs. We show that the discrete adjoint state trajectories converge to their continuous counterparts. Next, we describe the application of the proposed procedure to three optimal control problems. The first problem concerns optimal control of a simple mechanical system with dry friction. The second problem is related to the planning of a haemodialysis process. The third problem concerns the optimal steering of a racing car.