Semiconcave functions, Hamilton-Jacobi equations, and optimal control /
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control...
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| Format: | eBook |
| Language: | English |
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Boston :
Birkhäuser,
[2004]
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| Series: | Progress in nonlinear differential equations and their applications ;
v. 58. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and HamiltonJacobi equations. The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions. A central role in the present work is reserved for the study of singularities. Singularities are first investigated for general semiconcave functions, then sharply estimated for solutions of HamiltonJacobi equations, and finally analyzed in connection with optimal trajectories of control systems. Researchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions. Graduate students will profit from this text as it provides a handyyet rigorousintroduction to modern dynamic programming for nonlinear control systems. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xii, 304 pages) |
| Bibliography: | Includes bibliographical references (pages [295]-304) and index. |
| ISBN: | 9780817644130 (electronic bk.) 081764413X (electronic bk.) |