Titlebook: Representation and Control of Infinite Dimensional Systems; Alain Bensoussan,Giuseppe Prato,Sanjoy K. Mitter Book 2007Latest edition Birkh

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Unbounded Control Operators: Hyperbolic Equations With Control on the Boundaryse state .(·) is the solution of the following equation: . where . ∈ .(0, .;.) and .: .(.) ⊂ . → . generates a strongly continuous group on .. We identify the elements of .′ with those of . so that the linear operator (.*)*: . → .(.*)′ is a linear extension of the linear operator .: .(.) → .. As in

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Unbounded Control Operators: Parabolic Equations With Control on the Boundaryume that . Clearly, if hypotheses . hold, then the hypotheses . of Chapter 2 of Part IV are fulfilled with . = 0. If α ≤ 1/2, we will choose once and for all a number β belonging to ]1 − α/2, 1 − α/2[. We want to minimize the cost function: . over all controls . ∈ .(0,∞;.) subject to the differentia

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正论

Book 2007Latest editiond of Control of in?nite dim- sional systems. This was motivated by a whole range of challenging appli- tions arising from new phenomenologicalstudies, technologicaldevelopments, and more stringent design requirements. At the same time, researchers and advanced engineers have been steadily using an i

Multiple

Unbounded Control Operators: Hyperbolic Equations With Control on the Boundary.−.)., where . ∈ . and λ. is an element in ρ(.). More precisely, following . and . [1, 2, 11], we shall assume that . If assumptions . hold, then we can give a precise meaning to the state equation. We have in fact the following result due to . and

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Unbounded Control Operators: Parabolic Equations With Control on the Boundaryl equation constraint (1.1). We say that the control . ∈ .(0,∞;.) is . if .(.) < ∞. The definitions of optimal control, optimal state, and optimal pair are the same as in Chapter 1. When, for any . ∈ ., an admissible control exists, we say that (.) is C-stabilizable.

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