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Article

Glizer, Valery Y.
Singularly perturbed set of periodic functional-differential equations arising in optimal control theory. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 147-156
MSC: 34H05, 34K13, 34K26, 35F50
Keywords:
Periodic linear-quadratic optimal control problem, singularly perturbed delay system, small delay, periodic functional-differential matrix Riccati equations, asymptotic solution
Summary:
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
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