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Periodic Feedback Stabilization for Linear Periodic Evolution Equations.

By: Wang, Gengsheng.
Contributor(s): Xu, Yashan.
Material type: TextTextSeries: eBooks on Demand.SpringerBriefs in Mathematics: Publisher: Cham : Springer International Publishing, 2017Copyright date: ©2016Description: 1 online resource (135 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9783319492384.Subject(s): Periodic functionsGenre/Form: Electronic books.Additional physical formats: Print version:: Periodic Feedback Stabilization for Linear Periodic Evolution EquationsDDC classification: 510 LOC classification: QA353.P4.W364 2016Online resources: Click here to view this ebook.
Contents:
Preface -- Contents -- Acronyms -- 1 Controlled Periodic Equations, LQ Problems and Periodic Stabilization -- 1.1 Controlled Periodic Evolution Equations -- 1.2 Linear Quadratic Optimal Control Problems -- 1.2.1 Finite Horizon Case -- 1.2.2 Infinite Horizon Case -- 1.3 Relation Between Periodic Stabilization and LQ Problems -- 2 Criteria on Periodic Stabilization in Infinite Dimensional Cases -- 2.1 Attainable Subspaces -- 2.2 Three Criterions on Periodic Feedback Stabilization -- 2.2.1 Multi-periodic Feedback Stabilization -- 2.2.2 Proof of Theorem 2.1 -- 2.3 Applications -- 2.3.1 Feedback Realization in Finite Dimensional Subspaces -- 2.3.2 Applications to Heat Equations -- 3 Criteria on Periodic Stabilization in Finite Dimensional Cases -- 3.1 Null Controllable Subspaces -- 3.2 Algebraic Criterion and Application -- 3.2.1 The Proof of (a)(c) in Theorem 3.1 -- 3.2.2 The Proof of (a)(b) in Theorem 3.1 -- 3.2.3 Decay Rate of Stabilized Equations -- 3.3 Geometric Criterion -- 4 Design of Simple Control Machines -- 4.1 The First Kind of Simple Control Machines -- 4.2 The Second Kind of Simple Control Machines--General Case -- 4.3 The Second Kind of Simple Control Machines--Special Case -- Appendix References -- Index.
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Preface -- Contents -- Acronyms -- 1 Controlled Periodic Equations, LQ Problems and Periodic Stabilization -- 1.1 Controlled Periodic Evolution Equations -- 1.2 Linear Quadratic Optimal Control Problems -- 1.2.1 Finite Horizon Case -- 1.2.2 Infinite Horizon Case -- 1.3 Relation Between Periodic Stabilization and LQ Problems -- 2 Criteria on Periodic Stabilization in Infinite Dimensional Cases -- 2.1 Attainable Subspaces -- 2.2 Three Criterions on Periodic Feedback Stabilization -- 2.2.1 Multi-periodic Feedback Stabilization -- 2.2.2 Proof of Theorem 2.1 -- 2.3 Applications -- 2.3.1 Feedback Realization in Finite Dimensional Subspaces -- 2.3.2 Applications to Heat Equations -- 3 Criteria on Periodic Stabilization in Finite Dimensional Cases -- 3.1 Null Controllable Subspaces -- 3.2 Algebraic Criterion and Application -- 3.2.1 The Proof of (a)(c) in Theorem 3.1 -- 3.2.2 The Proof of (a)(b) in Theorem 3.1 -- 3.2.3 Decay Rate of Stabilized Equations -- 3.3 Geometric Criterion -- 4 Design of Simple Control Machines -- 4.1 The First Kind of Simple Control Machines -- 4.2 The Second Kind of Simple Control Machines--General Case -- 4.3 The Second Kind of Simple Control Machines--Special Case -- Appendix References -- Index.

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