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

Andras Varga, Stefan Johansson, Bo Kågström, Anton Shiriaev
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. The first problem arises from a stabilization problem for an artificially constructed time-varying linear system for which the exact solution is known. The second problem originates from a nonlinear stabilization problem for a devil stick juggling model along a periodic trajectory. The numerical comparisons have been 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 recently published algorithms for computing a reordered periodic real Schur form. The obtained results show the increased accuracy achievable by combining multi-shot methods with structure preserving (symplectic) integration techniques.
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