We derive closed-form extensions of Riccati's recursions (both sequential and parallel) for solving dual-regularized LQR problems. We show how these methods can be used to solve general constrained, non-convex, discrete-time optimal control problems via a regularized interior point method, while guaranteeing that each primal step is a descent direction of an Augmented Barrier-Lagrangian merit function. We provide MIT-licensed implementations of our methods in C++ and JAX.

翻译：本文推导了用于求解双正则化线性二次调节器（LQR）问题的Riccati递推（包括串行与并行形式）的闭式扩展。我们展示了如何通过正则化内部点方法，利用这些方法求解一般约束、非凸、离散时间最优控制问题，同时保证每个原始迭代步均为增广障碍-拉格朗日价值函数的下降方向。我们在C++和JAX中提供了基于MIT许可证的开源实现。