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Semiconcave functions, Hamilton-Jacobi equations, and optimal control
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Semiconcave functions, Hamilton-Jacobi equations, and optimal control

Semiconcave functions, Hamilton-Jacobi equations, and optimal control

Piermarco Cannarsa, Carlo Sinestrari

304 pages, parution le 02/06/2004

Résumé

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 Hamilton-Jacobi 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 Hamilton-Jacob! 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 handy-yet rigorous-introduction to modern dynamic programming for nonlinear control systems.

Sommaire

  • A model problem
  • Semiconcave functions
  • Generalized gradients and semiconcavity
  • Singularities of semiconcave functions
  • Hamilton-Jacobi equations
  • Calculus of variations
  • Optimal control problems
  • Control problems with exit time
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Piermarco Cannarsa, Carlo Sinestrari
Parution 02/06/2004
Nb. de pages 304
Format 16 x 24
Couverture Relié
Poids 600g
Intérieur Noir et Blanc
EAN13 9780817640842
ISBN13 978-0-8176-4084-2

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