On the existence of ε-optimal trajectories of the control systems with constrained control resources

Year 2017, Volume: 66 Issue: 1, 75 - 84, 01.02.2017

Anar Huseyın

https://doi.org/10.1501/Commua1_0000000776

Abstract

The control system described by a Urysohn type integral equationis considered. It is assumed that the admissible control functions are chosenfrom the closed ball of the space Lp; p > 1;with radius r and centered atthe origin. Precompactness of the set of trajectories of the control system inthe space of continuous functions is shown. This allows to prove that optimalcontrol problem with lower semicontinuous payoğ functional has an "-optimaltrajectory for every " > 0

Keywords

Urysohn integral equation, control system, integral constraint, set oftrajectories, "-optimal trajectory

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