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Controllability and observability of non autonomous evolution equations

Abstract : This thesis is devoted to the controllability and observability of nonautonomous evolution equation. In the first part, we give an overview on control theory as well as some classical results on control of both autonomous and nonautonomous systems. In fact, we will recall the technique in semigroup theory, evolution familys theory, duality theory and operator theory. In the second part, we are interested to investigate the control problem for PDEs systems defined on time-dependent domains. We develope some new techniques to obtain the results on exact observability for one dimensional wave and Schrödinger equations, then by duality we establish exact controllability of adjoint system. The last result is a generalization of Hautus tests for observability of non- autonomous evolution system.Our method can apply for Schrodinger equations with time dependent potentials and to a damped wave-equation with time-dependent damping.
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Duc-Trung Hoang. Controllability and observability of non autonomous evolution equations. Optimization and Control [math.OC]. Université de Bordeaux, 2018. English. ⟨NNT : 2018BORD0083⟩. ⟨tel-01898943⟩

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