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Optimal control of ordinary differential equations. (English) Zbl 1094.49001
Cañada, A.(ed.) et al., Ordinary differential equations. Vol. II. Amsterdam: Elsevier/North Holland (ISBN 0-444-52027-9/hbk). Handbook of Differential Equations, 1-75 (2005).
The book consists of four sections. In Section 1 principles of the classical Calculus of Variations are given. Section 2 contains elements of convex analysis and generalized differential calculus for locally Lipschitz functions, introduced by F. Clarke. Moreover, here is formulated Ekeland’s variational principle and basic facts of differential geometry and exponential representation of flows, introduced by A. Agrachev and R. Gamkrelidze are presented. Section 3 is concerned with the Pontryagin maximum principle for general Bolza problems and its applications. Here due to F. Clarke the maximum principle is proved. Moreover some aspects of geometric control theory are considered. In Section 4 the dynamic programming method in optimal control problems based on the Bellman equation is presented. Applications to linear-quadratic problems are given. I am certain that the book will be interesting for a broad readership.
For the entire collection see [Zbl 1074.34003].

MSC:
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49K15 Optimality conditions for problems involving ordinary differential equations
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49N10 Linear-quadratic optimal control problems
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