Comparing one-shot and multi-shot methods for solving periodic of Riccati differential equations

Abstract

Abstract - One-shot methods and recently proposed multi-shot methods for computing stabilizing solutions of continuoustime periodic Riccati differential equations are examined and evaluated on two test problems. The first problem arises from a stabilization problem for an artificially constructed time-varying linear systems for which the exact solution is known. The second problem originates from a nonlinear stabilization problem for numercial comparisons have been performed using both general purpose and symplectic integration methods for solving the associated Hamiltontian differential systems. In the multi-shot method a stable subspace is determined using recently published algorithms for computing a reodered periodic real Schur form. The obtained results show the increased accuracy achievable by combining multi-shot methods with structure preserving (symplectic) integration techniques.