Title Distributed systems with persistent memory : control and moment problems / Luciano Pandolfi

Published Cham : Springer, 2014

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Description 1 online resource (ix, 152 pages) : illustrations (some color) Series SpringerBriefs in Electrical and Computer Engineering, Control, Automation and robotics, 2191-8112 SpringerBriefs in electrical and computer engineering. Control, automation and robotics. Contents 880-01 An Example -- The Model and Preliminaries -- Moment Problems and Exact Controllability -- Controllability of the Wave Equation -- Systems with Persistent Memory: Controllability via Moment Methods -- Systems with Persistent Memory: The Observation Inequality 880-01/(S Machine generated contents note: 1. Example -- 1.1. Goal of This Chapter and Preliminaries -- 1.2. System with Persistent Memory -- 1.2.1. Finite Propagation Speed -- 1.2.2. Formula for the Solutions and a Control Problem -- 1.3. Background of Functional Analysis -- 1.3.1. Weak Topology in a Hilbert Spaces -- 1.3.2. Operators and Resolvents -- 1.3.3. Compact Operators -- 1.3.4. Fixed Point and Equations -- 1.3.5. Volterra Integral Equations -- 1.3.6. Test Functions and Distributions -- 1.3.7. Sobolev Spaces -- 1.3.8. Sobolev Spaces and the Laplace Operator -- 1.4. Problems to Chap. 1 -- 2. Model and Preliminaries -- 2.1. Goal of This Chapter and the System with Persistent Memory -- 2.1.1. Wave Equation -- 2.2. Solutions of the System with Memory -- 2.3. Description of the Control Problems -- 2.4. Useful Transformations -- 2.4.1. Finite Propagation Speed -- 2.5. Final Comments -- 2.6. Derivation of the Models -- 2.6.1. Thermodynamics with Memory and Nonfickian Diffusion -- 2.6.2. Viscoelasticity -- 2.6.3. Special Case of the Telegraphers' Equation -- 2.7. Problems to Chap. 2 -- 3. Moment Problems and Exact Controllability -- 3.1. Goal of This Chapter and the Moment Problem -- 3.1.1. Worked Example -- 3.2. Properties of the Moment Operator When Y = l2 -- 3.3. Riesz Sequences and Moment Problems -- 3.4. Perturbations of Riesz Sequences -- 3.4.1. Riesz Sequences of Exponentials in L2 Spaces -- 3.4.2. Second Worked Example -- 3.5. Problems to Chap. 3 -- 4. Controllability of the Wave Equation -- 4.1. Introduction and the Goal of This Chapter -- 4.2. Hidden Regularity and Observation Inequality -- 4.2.1. Consequences of Controllability on the Eigenvectors -- 4.3. Controllability and Moment Problem -- 4.4. Problems to Chap. 4 -- 5. Systems with Persistent Memory: Controllability via Moment Methods -- 5.1. Introduction and the Goal of This Chapter -- 5.2. Moment Problem and Controllability of Viscoelastic Systems -- 5.3. Proof of Controllability -- 5.3.1. Step A: the Functions Zn(t) and Rn(t) -- 5.3.2. Step B: Closeness to a Riesz Sequence -- 5.3.3. Step C: ω-Independence -- 5.4. Application: Source Identification -- 5.5. Problems to Chap. 5 -- 6. Systems with Persistent Memory: The Observation Inequality -- 6.1. Introduction and the Goal of This Chapter -- 6.2. Hidden Regularity for Systems with Persistent Memory, and a Test for the Solutions -- 6.2.1. Controllability and the Observation Inequality -- 6.3. Observation Inequality for Systems with Memory -- 6.3.1. Step A: Extension and Derivatives of the Solutions -- 6.3.2. Step B: Propagation of Singularities -- 6.3.3. Step C: End of the Proof -- 6.4. Problems to Chap. 6 Summary The subject of the book includes the study of control problems for systems which are encountered in viscoelasticity, non-Fickian diffusion and thermodynamic with memory. The common feature of these systems is that memory of the whole past history persists in the future. This class of systems is actively studied now, as documented in the recent book. This book will attract a diversified audience, in particular, engineers working on distributed systems, and applied mathematicians. Background of mathematics are the elements of functional analysis, which is now standard among people working on distributed systems, and the author describes very clearly the instruments which are used at every step Analysis systemen systems wiskunde mathematics functionaalanalyse functional analysis regeltheorie control theory Mathematics (General) Wiskunde (algemeen) Bibliography Includes bibliographical references and index Notes English Online resource; title from PDF title page (SpringerLink, viewed December 10, 2014) Subject Control theory. Distributed parameter systems. Moment problems (Mathematics) SCIENCE -- System Theory. TECHNOLOGY & ENGINEERING -- Operations Research. Teoría de control Momentos, Problema de los (Matemáticas) Control theory Distributed parameter systems Moment problems (Mathematics) Form Electronic book ISBN 9783319122472 3319122479 3319122460 9783319122465

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