A Generalization of the Riccati Recursion for Equality-Constrained Linear Quadratic Optimal Control

TL;DR

This paper presents a generalized Riccati recursion method for solving equality-constrained linear quadratic optimal control problems, enabling efficient computation of solutions and feedback policies without restrictive conditions.

Contribution

It introduces a novel, regularity-condition-free Riccati recursion that scales linearly and improves computational speed for constrained optimal control problems.

Findings

Achieves up to 100x speed-up over existing solvers

Scales linearly with horizon length

Applicable to nonlinear optimal control with exact Hessian info

Abstract

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal feedback control policies. Unlike other tailored approaches for this problem class, the proposed method does not require restrictive regularity conditions on the problem. This allows its use in nonlinear optimal control problem solvers that use exact Lagrangian Hessian information. We demonstrate that our approach can be implemented in a highly efficient algorithm that scales linearly with the horizon length. Numerical tests show a significant speed-up of up to two orders of magnitude with respect to state-of-the-art general-purpose sparse linear solvers. Based on the proposed approach, faster nonlinear optimal control problem solvers can be developed that are suitable for more complex applications or for implementations on low-cost or low-power computational platforms. The implementation of the proposed algorithm is made available as open-source software.