Stabilization of infinite dimensional systems / / El Hassan Zerrik, Oscar Castillo

• Record Nr.: UNINA9910483294703321
• Autore: Zerrik El Hassan
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-68600-0
• Descrizione fisica: 1 online resource (xii, 315 pages) : illustrations
• Collana: Studies in systems, decision and control ; ; Volume 355
• Disciplina: 006.3
• Soggetti: Computational intelligence; Automatic control
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- Notations -- 1 Introduction -- References -- 2 Stabilization of Infinite Dimensional Linear Systems -- 2.1 Linear Semigroups -- 2.2 Stability of Infinite Dimensional Linear Systems -- 2.2.1 Definitions-Examples -- 2.2.2 Characterizations -- 2.3 Stabilization of Infinite Dimensional Linear Systems -- 2.3.1 Characterizations -- 2.3.2 Optimal Stabilization Problem -- References -- 3 Stabilization of Infinite Dimensional Semilinear Systems -- 3.1 Well Posed Systems -- 3.2 Stabilization of Infinite Dimensional Bilinear Systems -- 3.3 Stabilization of Infinite Dimensional Semilinear Systems -- 3.3.1 Existence and Uniqueness Results -- 3.3.2 Stabilization Results -- References -- 4 Regional Stabilization of Infinite Dimensional Linear Systems -- 4.1 Internal Regional Stability -- 4.1.1 Definitions -- 4.1.2 Examples -- 4.1.3 Characterization of Regional Stability -- 4.2 Internal Regional Stabilization -- 4.2.1 Definitions -- 4.2.2 Characterizations -- 4.2.3 Regional Stabilizing Control -- 4.2.4 Low Cost Regional Stabilization Problem -- 4.3 Numerical Examples -- 4.3.1 One Dimensional Case -- 4.3.2 Two Dimensional Case -- 4.4 Regional Boundary Stabilization -- 4.5 Optimal Control for Regional Boundary Stabilization -- 4.5.1 Direct Approach -- 4.5.2 Internal Approach -- References -- 5 Regional Stabilization of Infinite Dimensional Bilinear Systems -- 5.1 Regional Stabilization -- 5.1.1 Regional Exponential Stabilization -- 5.1.2 Regional Weak Stabilization ; -- 5.1.3 Regional Strong Stabilization -- 5.2 Regional Stabilization Problem -- 5.2.1 Case of Isometries Semigroup -- 5.2.2 Case of Contractions Semigroup -- 5.3 Simulation Results -- References -- 6 Regional Stabilization of Infinite Dimensional Semilinear Systems -- 6.1 Regional Stabilization -- 6.1.1 Regional Exponential Stabilization.; 6.1.2 Regional Strong Stabilization -- 6.1.3 Regional Weak Stabilization -- 6.2 Regional Stabilization Problem -- 6.3 Simulation Results -- References -- 7 Output Stabilization of Infinite Dimensional Semilinear Systems -- 7.1 Output Stabilization of Semilinear Systems -- 7.1.1 Output Exponential Stabilization -- 7.1.2 Output Strong Stabilization -- 7.1.3 Output Weak Stabilization -- 7.2 Output Stabilization of Bilinear Systems -- 7.2.1 Output Exponential Stabilization -- 7.2.2 Output Strong Stabilization -- 7.2.3 Output Weak Stabilization -- 7.2.4 Examples -- 7.3 Simulations -- References -- 8 Stabilization of Infinite Dimensional Second Order Semilinear Systems -- 8.1 Stabilization of Bilinear Systems -- 8.1.1 Strong Stabilization -- 8.1.2 Exponential Stabilization -- 8.2 Stabilization of Semilinear Systems -- 8.2.1 Strong Stabilization -- 8.2.2 Exponential Stabilization -- 8.3 Regional Stabilization of Second Order Semilinear Systems -- 8.3.1 Regional Stabilization of Bilinear Systems -- 8.3.2 Regional Stabilization of Semilinear Systems -- 8.4 Simulations Results -- References -- 9 Gradient Stabilization of Infinite Dimensional Linear Systems -- 9.1 Gradient Stability-Definitions-Examples -- 9.2 Characterizations of Gradient Stability -- 9.3 Gradient Stabilization for Infinite Dimensional System -- 9.3.1 State Space Decomposition -- 9.3.2 Riccati Method -- 9.4 Gradient Stabilization Control Problem -- 9.5 Numerical Algorithm and Simulations -- References -- 10 Regional Gradient Stabilization of Infinite Dimensional Linear Systems -- 10.1 Regional Gradient Stability -- 10.1.1 Definitions -- 10.1.2 Characterizations -- 10.2 Gradient Stabilization -- 10.2.1 Stabilizing Control -- 10.2.2 State Space Decomposition -- 10.2.3 Lower Cost Gradient Stabilization Problem -- 10.2.4 Numerical Approach and Simulations -- References.; 11 Gradient Stabilization of Infinite Dimensional Bilinear Systems -- 11.1 Gradient Stabilization of Bilinear Systems -- 11.1.1 Gradient Exponential Stabilization -- 11.1.2 Gradient Strong Stabilization -- 11.1.3 Gradient Weak Stabilization -- 11.2 Regional Gradient Stabilization of Bilinear Systems -- 11.2.1 Regional Stabilizing Control -- 11.2.2 State Space Decomposition -- 11.2.3 Problem of Regional Gradient Stabilization -- 11.3 Numerical Approach and Simulations -- 11.3.1 Regional Gradient Stabilization Case -- 11.3.2 Gradient Stabilization Case -- References -- 12 Regional Gradient Stabilization of Infinite Dimensional Semilinear Systems -- 12.1 Controls for Regional Gradient Stabilization -- 12.1.1 Regional Gradient Strong Stabilization -- 12.1.2 Regional Gradient Weak Stabilization -- 12.2 Regional Gradient Stabilization Problem -- 12.3 Simulation Results -- References -- 13 Conclusion and Perspectives -- Appendix References -- -- Index.