A Constraint Homotopy Active Set Solver for Linear-Quadratic Optimal Control

An efficient optimization method is proposed for linear- quadratic optimal control problems with state and control constraints. We describe an active set solver that uses Riccati recursions to solve a sequence of equality-constrained subproblems. The main contribution is a homotopy method based on relaxing inequality constraints. This overcomes known shortcomings of Riccati active set solvers relating to their initialisation and their application to problems with time-varying model data. It can be used exclusively or in combination with established Riccati active set solvers. The efficiency is demonstrated in numerical examples against state-of-the-art quadratic programming solvers.