On the Implementation of a Preconditioned Riccati Recursion based Primal-Dual Interior-Point Algorithm for Input Constrained Optimal Control Problems⋆

Abstract

We present a preconditioned interior-point algorithm tailored for input constrained quadratic programmings (QPs) arising in optimal control problems (OCPs). The implicit approach to OCPs results in large sparse QPs, which we utilized by a tailored Riccati recursion algorithm. The Riccati recursion algorithm requires the solution of a set of small dense linear sub-systems of equations. The proposed preconditioner is an easily invertible diagonal matrix, which we apply in every linear sub-system of equations. We solve a target tracking OCP for a linearized modified quadruple tank system in Matlab. The computational results indicate that ill-conditioning in the sub-systems are reduced and that the additional CPU time for preconditioning is negligible. Additionally, the paper presents a detailed description of the proposed algorithm and serves as an implementation guide for the algorithm.