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Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets. (English) Zbl 0712.49015
Nonlinear controllability and optimal control, Lect. Workshop, New Brunswick/NJ (USA) 1987, Pure Appl. Math., Marcel Dekker 133, 1-19 (1990).
[For the entire collection see Zbl 0699.00040.]
The basic concepts of optimal presynthesis and synthesis for optimal control problems described by the system \(\dot x=f(x,u)\) are explained. It is shown how the theory of subanalytic sets can be used to prove existence theorems. Furthermore the link with several other papers is established by showing how the results on synthesis lead to the search for theorems on the structure of optimal trajectories.
Reviewer: H.Benker

49K15 Optimality conditions for problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations