A Regularized Riccati Recursion for Interior-Point Optimal Control

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