Constrained LQR Design Using Interior-Point Arc-Search Method for Convex Quadratic Programming with Box Constraints

TL;DR

This paper introduces an efficient interior-point arc-search algorithm tailored for convex quadratic programming with box constraints, specifically applied to constrained LQR design, demonstrating improved computational complexity and practical effectiveness.

Contribution

It develops a novel arc-search interior-point method exploiting box constraint structure for constrained LQR, with proven polynomial complexity and successful MATLAB implementation.

Findings

Algorithm is polynomial with optimal complexity bounds.

Effective for constrained LQR and adaptable to model predictive control.

MATLAB implementation demonstrates practical efficiency.

Abstract

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.