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49-02 Calculus of variations and optimal control; optimization -- Research exposition (monographs, survey articles)

37Gxx Dynamical systems and ergodic theory -- Local and nonlocal bifurcation theory

49K30 Calculus of variations and optimal control; optimization -- Optimality conditions -- Optimal solutions belonging to restricted classes

93Dxx Systems theory; control -- Stability En-ligne: Springerlink | Zentralblatt | MathSciNet

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The book is devoted to the study of branching points of extremal solutions of an optimal control problem. For nonlinear control problems the branching points with respect to neighboring trajectories are considered. The main result is that under suitable hypotheses the set of the branching points depends on the system (on the linearized system in the nonlinear case) and not on the cost functional. The cases of vector cost and a constrained set of admissible controls are also considered. (Zentralblatt)

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