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Feedback necessary optimality conditions for nonlinear measure-driven processes

Авторы: Samsonyuk O.N., Sorokin S.P., Staritsyn M.V.

Журнал: IFAC-PapersOnLine

Том: 52

Номер: 16

Год: 2019

Отчётный год: 2020

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Аннотация: We consider a non-convex optimal impulsive control problem for nonlinear differential equations, driven by vector-valued Borel measures, under no commutativity assumptions of the Frobenius type. For this problem, we derive nonlocal necessary optimality conditions operating with a specific class of impulsive feedback controls, generated by certain functions of the Lyapunov type. These feedback controls are constructed in a way similar to the dynamical programming, but with the use of weakly monotone solutions to the corresponding Hamilton-Jacobi equation, instead of the Bellman’s function. We offer the notion of weakly monotone function with respect to a measure-driven differential equation, and give constructive criteria for this type of monotonicity. Based on a space-time representation of impulsive processes, we propose the concept of impulsive feedback control and present nonlocal necessary optimality conditions, which are shown to filter out non-optimal extrema of the impulsive Maximum Principle.

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