Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
2004
|
| Series: | Progress in Nonlinear Differential Equations and Their Applications
58 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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–Jacobi 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 |
| Physical Description: | 1 Online-Ressource (XIV, 304 p) |
| ISBN: | 9780817644130 9780817643362 |
| DOI: | 10.1007/b138356 |
Staff View
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817644130 9780817643362 |
| language | English |
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| publisher | Birkhäuser Boston |
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| series2 | Progress in Nonlinear Differential Equations and Their Applications |
| spelling | Cannarsa, Piermarco 1957- Verfasser (DE-588)17369361X aut Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control by Piermarco Cannarsa, Carlo Sinestrari Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XIV, 304 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 58 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–Jacobi 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 Mathematics Differential equations, partial Mathematical optimization Partial Differential Equations Measure and Integration Optimization Mathematik Konkave Optimierung (DE-588)4306302-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd rswk-swf Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 s Optimale Kontrolle (DE-588)4121428-6 s 1\p DE-604 Konkave Optimierung (DE-588)4306302-0 s 2\p DE-604 Sinestrari, Carlo 1970- Sonstige (DE-588)141301473 oth https://doi.org/10.1007/b138356 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cannarsa, Piermarco 1957- Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control Mathematics Differential equations, partial Mathematical optimization Partial Differential Equations Measure and Integration Optimization Mathematik Konkave Optimierung (DE-588)4306302-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd |
| subject_GND | (DE-588)4306302-0 (DE-588)4121428-6 (DE-588)4158954-3 |
| title | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control |
| title_auth | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control |
| title_exact_search | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control |
| title_full | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control by Piermarco Cannarsa, Carlo Sinestrari |
| title_fullStr | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control by Piermarco Cannarsa, Carlo Sinestrari |
| title_full_unstemmed | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control by Piermarco Cannarsa, Carlo Sinestrari |
| title_short | Semiconcave Functions, Hamilton - Jacobi Equations, and Optimal Control |
| title_sort | semiconcave functions hamilton jacobi equations and optimal control |
| topic | Mathematics Differential equations, partial Mathematical optimization Partial Differential Equations Measure and Integration Optimization Mathematik Konkave Optimierung (DE-588)4306302-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Hamilton-Jacobi-Differentialgleichung (DE-588)4158954-3 gnd |
| topic_facet | Mathematics Differential equations, partial Mathematical optimization Partial Differential Equations Measure and Integration Optimization Mathematik Konkave Optimierung Optimale Kontrolle Hamilton-Jacobi-Differentialgleichung |
| url | https://doi.org/10.1007/b138356 |
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