Sequential differentiation and its applications in optimal control problems

S. Ya. Serovaĭskiĭ

Kazakh National University, Almaty, Republic of Kazakhstan

Abstract: Using the sequential approach, we define a certain generalization of the operator derivative. We establish the necessary extremum condition in terms of the sequential derivative. As examples we consider the optimal control problems for systems governed by partial nonlinear differential equations of several kinds.

Keywords: operator differentiation, sequential approach, optimality conditions.

UDC: 571.98

Received: 23.05.2006

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:7, 38–47

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