Dual-Regularized Riccati Recursions for Interior-Point Optimal Control
João Sousa-Pinto, Dominique Orban
TL;DR
The paper addresses solving constrained, non-convex discrete-time optimal control problems efficiently by deriving closed-form, dual-regularized Riccati recursions. It develops both sequential and parallel algorithms that arise from applying a regularized interior-point method to OCPs and reducing the subproblems to a dual-regularized LQR, guaranteeing descent via the Augmented Barrier-Lagrangian merit function. Key contributions include the backward recursion with positive semi-definite $P_k$, forward recovery formulas, and a parallel Riccati recursion built through associative scans and interval value functions, plus residual computation for iterative refinement. The authors provide open-source, MIT-licensed implementations in both C++ and JAX, enabling practical, scalable solutions for constrained OCPs in robotics, aerospace, and other domains. The work offers a principled bridge between interior-point optimization and classical Riccati-based control, delivering both theoretical guarantees and usable software artifacts.
Abstract
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.