We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints. This is the first such exact algorithm that is guaranteed to have a runtime that is linear in the number of stages, as well as linear in the number of both state-only constraints as well as mixed state-and-control constraints, without imposing any restrictions on the problem instances. We also show how to easily parallelize this algorithm to run in parallel runtime logarithmic in the number of stages of the problem.

翻译：本文提出了一种求解带线性等式约束的线性二次调节器（LQR）问题的新算法。这是首个保证运行时间随阶段数线性增长，且随纯状态约束及状态-控制混合约束数量线性增长的精确算法，且不对问题实例施加任何限制。我们还展示了如何轻松并行化该算法，使其并行运行时间与问题阶段数呈对数关系。