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Optimal synthesis for nonoscillatory controlled objects. (English) Zbl 0958.49012
Summary: We consider nonlinear, nonoscillatory controlled objects of second-order. The main theorem affirms that for these controlled objects there exist (in the controllability region) the time-optimal synthesis of Feldbaum’s type. In the beginning of the paper, Feldbaum’s $$n$$-interval theorem is proved for linear controlled objects of $$n$$th-order with real eigenvalues (and without the requirement that the eigenvalues are pairwise distinct).
##### MSC:
 49K15 Optimality conditions for problems involving ordinary differential equations 93C15 Control/observation systems governed by ordinary differential equations 49L20 Dynamic programming in optimal control and differential games
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