A Regularized Riccati Recursion for Interior-Point Optimal Control

2025-09-19

AI Summary

This paper addresses constrained, non-convex discrete-time optimal control problems. We propose an interior-point method framework built upon regularized Riccati recursion—a novel integration of the numerically stable Riccati backward pass from regularized linear-quadratic regulators (LQR) into the interior-point optimization loop. Each iteration updates the primal-dual variables along a strict descent direction of an augmented barrier–Lagrangian merit function, ensuring both numerical stability and global convergence. Unlike conventional nonlinear programming approaches, our method avoids explicit Hessian assembly and large-scale sparse linear system solves, substantially improving computational efficiency. The algorithm is implemented in both C++ and JAX and is publicly available under the MIT license. Extensive evaluation across diverse non-convex control benchmarks demonstrates superior robustness and real-time performance compared to state-of-the-art solvers.

Technology Category

Search and Optimization: Non-convex OptimizationConstraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationPlanning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

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Abstract

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.

Problem

• Solves regularized LQR problems using extended Riccati recursion
• Addresses constrained non-convex optimal control via interior point method
• Guarantees descent direction for Augmented Barrier-Lagrangian merit function

Innovation

• Regularized Riccati recursion for LQR problems
• Interior point method for constrained optimal control
• Augmented Barrier-Lagrangian merit function descent