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Quadratic Control for Stochastic Systems Defined by Evolution Operators and Square Integrable Martingales
Author(s) -
Tudor C.
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901470122
Subject(s) - mathematics , square integrable function , stochastic differential equation , integrable system , optimal control , quadratic equation , stochastic control , square (algebra) , algebraic riccati equation , convergence (economics) , martingale (probability theory) , stochastic calculus , riccati equation , mathematical analysis , stochastic partial differential equation , mathematical optimization , differential equation , geometry , economic growth , economics
The infinite dimensional version of the linear quadratic cost control problem is studied by Curtain and Pritchard [2], Gibson [5] by using Riccati integral equations, instead of differential equations. In the present paper the corresponding stochastic case over a finite horizon is considered. The stochastic perturbations are given by Hilbert valued square integrable martingales and it is shown that the deterministic optimal feedback control is also optimal in the stochastic case. Sufficient conditions are given for the convergence of approximate solutions of optimal control problems.