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Optimal control with a functional averaged along the trajectory. (English. Russian original) Zbl 0614.49015
J. Appl. Math. Mech. 49, 404-413 (1985); translation from Prikl. Mat. Mekh. 49, 524-535 (1985).
Consider a control problem in which the differential equation relating the state and control functions, as well as the integrand in the performance criterion, are not explicitely time-dependent. A set of infinite optimal trajectories (IOT) is defined. It is shown that in an arbitrary fixed-time interval any optimal trajectory can be uniformly approximated to some IOT with a desired accuracy, provided that the control time is fairly large.
Reviewer: J.Rubio

49K15 Optimality conditions for problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
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