Partially stabilizing LQ-optimal control for stabilizable semigroup systems |
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Authors: | Frank M Callier Laurence Dumortier |
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Institution: | (1) Department of Mathematics, Facultés Universitaires Notre-Dame de la Paix, 8, Rempart de la Vierge, B-5000 Namur, Belgium |
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Abstract: | The Linear-Quadratic optimal control problem with a partial stabilization constraint (LQPS) is considered for exponentially stabilizable infinite dimensional semigroup state-space systems with bounded sensing and control (having their transfer function with entries in the algebra
. It is reported that the LQPS-optimal state-feedback operator is related to a nonnegative self-adjoint solution of an operator Riccati equation and it can be identified (1) by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper-stable transfer function algebra
_, and (2) by obtaining any constant solution of a diophantine equation over
_. These theoretical results are applied to a simple model of heat diffusion, leading to an approximation procedure converging exponentially fast to the LQPS-optimal state feedback operator. |
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Keywords: | 49N05 49J22 93B52 93D15 93C05 93C25 47N70 47D06 47B65 49M99 |
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