An efficient algorithm for solving linear equality-constrained LQR problems

TL;DR

This paper introduces a new efficient algorithm for solving constrained linear-quadratic regulator problems, achieving linear sequential and logarithmic parallel runtimes by parallelizing constraint elimination while maintaining problem definiteness.

Contribution

The paper develops a novel parallelizable technique for eliminating linear equality constraints in LQR problems, improving computational efficiency.

Findings

Sequential runtime is linear in stages and constraints.

Parallel runtime is logarithmic in the number of stages.

The method preserves positive definiteness of the problem.

Abstract

We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and constraints, and its parallel runtime is logarithmic in the number of stages. The main technical contribution of this paper is the derivation of parallelizable techniques for eliminating the linear equality constraints while preserving the standard positive (semi-)definiteness requirements of LQR problems.