Strong Formulations for Hybrid System Control

TL;DR

This paper develops strong mixed-integer quadratic programming formulations for hybrid control problems, introducing new valid cuts that improve computational efficiency in solving complex energy management and hybrid system control tasks.

Contribution

The paper introduces novel convex hull descriptions and valid cuts for hybrid control problems, enhancing solution efficiency in mixed-integer quadratic programming formulations.

Findings

Significant reduction in computational effort for test instances.

Effective application of cuts to energy management problems.

Improved solution times for hybrid control problems.

Abstract

We study the mixed-integer quadratic programming formulation of an $n$-period hybrid control problem with a convex quadratic cost function and linear dynamics. We first give the convex hull description of the single-period, two-mode problem in the original variable space through two new classes of valid cuts. These cuts are then generalized to the single-period, multi-mode, multi-dimensional case and applied to solve the general $n$-period hybrid control problem. Computational experiments demonstrate the effectiveness of the proposed strong formulations derived through the cut generation process in the original variable space. These formulations yield a substantial reduction in computational effort for synthetic test instances and instances from the energy management problem of a power-split hybrid electric vehicle.