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.

翻译：本文提出了一种求解带线性等式约束的线性二次型调节器（LQR）问题的新算法，该问题亦称为约束LQR（CLQR）问题。本方法的串行运行时间随阶段数和约束数呈线性增长，并行运行时间随阶段数呈对数增长。本文的主要技术贡献在于推导了可并行化的约束消除技术，该技术在消除线性等式约束的同时，保持了LQR问题标准正定（半正定）性要求。