### Shape optimization of control problems described by wave equations

Andrzej Nowakowski (2008)

Control and Cybernetics

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Andrzej Nowakowski (2008)

Control and Cybernetics

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Leszek Mikulski (2004)

International Journal of Applied Mathematics and Computer Science

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Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand...

Daniel Hernández-Hernández, Onésimo Hernández-Lerma, Michael Taksar (1996)

Applicationes Mathematicae

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Given a deterministic optimal control problem (OCP) with value function, say ${J}^{*}$, we introduce a linear program $\left(P\right)$ and its dual $\left({P}^{*}\right)$ whose values satisfy $sup\left({P}^{*}\right)\le inf\left(P\right)\le {J}^{*}(t,x)$. Then we give conditions under which (i) there is no duality gap

(2005)

Control and Cybernetics

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Jaroslav Doležal, Ronald R. Mohler (1981)

Kybernetika

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Jiří V. Outrata, Otakar F. Kříž (1980)

Kybernetika

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Emmanuel Degryse, Stéphane Mottelet (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with a new method to control flexible structures by designing non-collocated sensors and actuators satisfying a pseudo-collocation criterion in the low-frequency domain. This technique is applied to a simply supported plate with a point force actuator and a piezoelectric sensor, for which we give some theoretical and numerical results. We also compute low-order controllers which stabilize pseudo-collocated systems and the closed-loop behavior show that this approach...