An indirect computational procedure for receding horizon hybrid optimal control

TL;DR

This paper introduces an indirect computational method for solving receding horizon hybrid optimal control problems, combining the hybrid maximum principle with a branch and bound algorithm to efficiently determine optimal controls.

Contribution

It presents a novel indirect approach that reduces the hybrid control problem to algebraic equations and employs a branch and bound algorithm for solution, improving computational efficiency.

Findings

The method accurately finds optimal controls within finite steps.

It outperforms existing methods in a case study.

The approach is applicable to affine hybrid systems.

Abstract

In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid system within the prediction horizon is composed of both discrete-valued sequences and continuous-valued time-trajectories. Given a cost functional, the optimal continuous trajectories can be calculated given the discrete sequences by the means of the recent results on the hybrid maximum principle. It is shown that these calculations reduce to solving a system of algebraic equations in the case of affine hybrid systems. Then, a branch and bound algorithm is proposed which determines both the discrete and continuous control inputs by iterating on the discrete sequences. It is shown that the algorithm finds the correct solution in a finite number of steps if the selected cost functional satisfies certain conditions. Efficiency of the proposed method is demonstrated during a case study through comparisons with the main existing method.