Comparing One-shot and Multi-shot Methods for Solving Periodic Riccati Differential Equations
2007 (English)In: Proceedings of the third IFAC Workshop on Periodic Control Systems (PSYCO’07), International Federation of Automatic Control , 2007, 1-6 p.Conference paper (Refereed)
One-shot methods and recently proposed multi-shot methods for computing stabilizing solutions of continuous-time periodic Riccati differential equations are examined and evaluated on two test problems: (i) a stabilization problem for an artificially constructed time-varying linear system for which the exact solution is known; (ii) a nonlinear stabilization problem for a devil stick juggling model along a periodic trajectory. The numerical comparisons are performed using both general purpose and symplectic integration methods for solving the associated Hamiltonian differential systems. In the multi-shot method a stable subspace is determined using recent algorithms for computing a reordered periodic real Schur form. The results show the increased accuracy achievable by combining multi-shot methods with structure preserving (symplectic) integration techniques.
Place, publisher, year, edition, pages
International Federation of Automatic Control , 2007. 1-6 p.
periodic systems, reordered periodic Schur form, Riccati differential equations, stabilizing controllers, linear quadratic regulators
Research subject Numerical Analysis
IdentifiersURN: urn:nbn:se:umu:diva-18477ISBN: 978-3-902661-30-2OAI: oai:DiVA.org:umu-18477DiVA: diva2:159860