On the SDP Relaxation of Direct Torque Finite Control Set Model Predictive Control

TL;DR

This paper introduces a semidefinite programming relaxation for direct-torque finite-control-set model predictive control, combining it with a branch-and-bound algorithm to improve torque transient performance in simulations.

Contribution

It presents a novel SDP relaxation method for long horizon control problems and integrates it with a branch-and-bound approach for enhanced control performance.

Findings

Significant improvements in torque transients observed in simulations

The combined approach outperforms traditional branch-and-bound methods

The relaxation reduces computational burden while maintaining control quality

Abstract

This paper formulates a semidefinite programming relaxation for a long horizon direct-torque finite-control-set model predictive control problem. In parallel with this relaxation, a conventional branch-and-bound algorithm tailored for the original problem, but with an iteration limit to restrict its computational burden, is also solved. An input sequence candidate is extracted from the solution of the semidefinite program in the lifted space. This sequence is then compared with the so-called early-stopping branch-and-bound solution, and the best of the two is applied in a receding horizon fashion. In simulated case studies, the proposed approach exhibits significant improvements in torque transients, as the branch-and-bound alone struggles to find a meaningful solution due to the imposed limit.