Controllability of Dynamic Systems : The Green's Function Approach.

Intro -- Contents -- List of Figures -- List of Tables -- Preface -- Acknowledgements -- List of Symbols -- 1. Introduction -- 1.1 Controllability -- 1.1.1 Exact Controllability -- 1.1.2 Approximate Controllability -- 1.1.3 Choice of the Set of Admissible Controls -- 1.1.4 Resolving Controls -- 1.1.5 Methods of Finding Resolving Controls -- 1.2 The Green's Function Method for Linear Systems -- 1.2.1 Particular Cases -- 1.3 The Green's Function Method for Nonlinear Systems -- 1.3.1 Cacuci's Approach -- 1.3.2 Frasca's Approach -- 1.4 The Green's Function Method in Controllability Analysis -- 2. Linear Systems -- 2.1 Problem Statement -- 2.2 Resolving System -- 2.2.1 Particular Cases: Exact Controllability -- 2.2.2 Particular Cases -- 2.3 Particular Solutions of the Resolving System -- 2.3.1 Exact Controllability -- 2.3.2 Approximate Controllability -- 2.4 Examples -- 2.4.1 Finite Thin Inhomogeneous Rod Heated from Both Ends -- 2.4.2 Semi-Infinite Rod Heated by a Point Source -- 2.4.3 Elastic Beam Subjected to a Dynamic Load with Uncertainty -- 2.4.4 Square Heated from the Boundary -- 3. Nonlinear Systems -- 3.1 Problem Statement -- 3.2 Resolving System -- 3.3 Examples -- 3.3.1 Pendulum with Cubic Non-Linea -- 3.3.2 Sine-Gordon Equation -- 3.3.3 Approximation Error Analysis -- 3.4 Burgers' Equation -- Summary -- Bibliography -- Index.

The book is about the possibilities of involvement of the well-known Green's function method in exact or approximate controllability analysis for dynamic systems. Due to existing extensions of the Green's function notion to nonlinear systems, the approach developed here is valid for systems with both linear and nonlinear dynamics. The book offers a number of particular examples, covering specific issues that make the controllability analysis sophisticated, such as coordinate dependent characteristics, point sources, unbounded domains, higher dimensions, and specific nonlinearities. It also offers extensive numerical analysis, which reveals both advantages and drawbacks of the approach. As such, the book will be of interest to researchers interested in the theory and practice of control, as well as PhD and Master's students.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.