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Optimal periodic control. (English) Zbl 0663.49011

Lecture Notes in Mathematics, 1313. Berlin etc.: Springer-Verlag. vi, 177 p. (1988).
This monograph considers optimal control problems in \(R^ n\) for systems described by ordinary differential equations. One looks for a \(\tau\)- periodic control function and trajectory so that the average cost over a period is minimized. The main topic of these notes is the relationship between this problem and one of steady-state optimization, consisting in finding a steady-state conrol and trajectory of the given system which minimize the integrand of the performance criterion. After treating optimization theory, the author deals with retarded functional differential equations and their control, using Ekeland’s variational principle. Finally, optimal periodic control is studied, ending with an example involving the controlled bifurcation in a tank reactor.
Reviewer: J.Rubio

MSC:

49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
34C25 Periodic solutions to ordinary differential equations
34K35 Control problems for functional-differential equations
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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