Time Optimal Control Of Evolution Equations
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Author | : Gengsheng Wang |
Publisher | : Springer |
Total Pages | : 344 |
Release | : 2018-08-22 |
Genre | : Science |
ISBN | : 331995363X |
This monograph develops a framework for time-optimal control problems, focusing on minimal and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal control problems. By discussing the best way of representing various control problems and equivalence among them, this systematic study gives readers the tools they need to solve practical problems in control. After introducing preliminaries in functional analysis, evolution equations, and controllability and observability estimates, the authors present their time-optimal control framework, which consists of four elements: a controlled system, a control constraint set, a starting set, and an ending set. From there, they use their framework to address areas of recent development in time-optimal control, including the existence of admissible controls and optimal controls, Pontryagin’s maximum principle for optimal controls, the equivalence of different optimal control problems, and bang-bang properties. This monograph will appeal to researchers and graduate students in time-optimal control theory, as well as related areas of controllability and dynamic programming. For ease of reference, the text itself is self-contained on the topic of time-optimal control. Frequent examples throughout clarify the applications of theorems and definitions, although experience with functional analysis and differential equations will be useful.
Author | : Noriaki Yamazaki |
Publisher | : |
Total Pages | : |
Release | : 2008 |
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Author | : Andrew Thomas Plant |
Publisher | : |
Total Pages | : 230 |
Release | : 1974 |
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Author | : Shouchuan Hu |
Publisher | : American Mathematical Soc. |
Total Pages | : 97 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 082180779X |
This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analysed.
Author | : A. Ichikawa |
Publisher | : |
Total Pages | : 29 |
Release | : 1977 |
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Author | : Felix Spura |
Publisher | : |
Total Pages | : |
Release | : 2019 |
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Author | : M. Hassan Farshbaf-Shaker |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : |
ISBN | : |
In this paper we study an optimal control problem for a doubly nonlinear evolution equation governed by time-dependent subdifferentials. We prove the existence of solutions to our equation. Also, we consider an optimal control problem without uniqueness of solutions to the state system. Then, we prove the existence of an optimal control which minimizes the nonlinear cost functional. Moreover, we apply our general result to some model problem.
Author | : Kaïs Ammari |
Publisher | : Cambridge University Press |
Total Pages | : 205 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 1108412300 |
The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.
Author | : Gengsheng Wang |
Publisher | : Springer |
Total Pages | : 135 |
Release | : 2017-02-08 |
Genre | : Science |
ISBN | : 3319492381 |
This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.
Author | : Herbert Amann |
Publisher | : Springer Science & Business Media |
Total Pages | : 643 |
Release | : 2008-02-28 |
Genre | : Mathematics |
ISBN | : 3764377941 |
Gunter Lumer was an outstanding mathematician whose works have great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips from 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Gunter Lumer.