Feasibility Evaluation of Quadratic Programs for Constrained Control

TL;DR

This paper introduces a fast and efficient method to evaluate the feasibility of quadratic programs in real-time constrained control by transforming the problem into a simpler linear program, outperforming existing approaches.

Contribution

The paper proposes a novel LP-based approach for QP feasibility assessment that is computationally more efficient and simpler than previous methods, enabling better online control.

Findings

The LP-based method reduces computation time for feasibility checks.

The approach is validated through comparative case studies.

It shows promise for real-time optimization-based control applications.

Abstract

This paper presents a computationally-efficient method for evaluating the feasibility of Quadratic Programs (QPs) for online constrained control. Based on the duality principle, we first show that the feasibility of a QP can be determined by the solution of a properly-defined Linear Program (LP). Our analysis yields a LP that can be solved more efficiently compared to the original QP problem, and more importantly, is simpler in form and can be solved more efficiently compared to existing methods that assess feasibility via LPs. The computational efficiency of the proposed method compared to existing methods for feasibility evaluation is demonstrated in comparative case studies as well as a feasible-constraint selection problem, indicating its promise for online feasibility evaluation of optimization-based controllers.