Strong Convergence and Convergence Rates of Approximating Solutions for Algebraic Riccati Equations in Hilbert Spaces*
نویسندگان
چکیده
Inthis paper, -we considersthe linear quadratic optimal control 4, problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces. The optimal control is given by a feedback form in terms of solution r1 to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence rl of finite dimensional approximations of the solution to ARE. A sufficient condition that shows liN converges strongly to I is obtained. Under this condition, we derive a formula which can be used to obtain a rate of convergence of 0" to n. We demonstrate and apply the results for the Galerkin approximation for parabolic systems and the averaging approximation for hereditary differential systems.
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