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Quadratic control for linear periodic systems. (English) Zbl 0647.93057
The authors consider linear periodic systems on Hilbert spaces and minimize the limsup of a quadratic average cost. Under stabilizability and detectability assumptions the form of the optimal feedback is given involving the unique T-periodic nonnegative solution of a Riccati equation. Next analogous results are proved for stochastic systems. Then for problems with partial observation a separation principle is derived. Finally several examples illustrate the results.
Reviewer: F.Colonius

MSC:
93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
93C25 Control/observation systems in abstract spaces
34C25 Periodic solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
46C99 Inner product spaces and their generalizations, Hilbert spaces
49L99 Hamilton-Jacobi theories
93E11 Filtering in stochastic control theory
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