Controlled Fractional Order Processes with Distributed Parameters

Abstract This work is devoted to the study of the problem of pursuit in systems controlled with distributed parameters of fractional order. Derivatives with respect to spatial variables are ordinary, integer, and even of arbitrary order. Designed and studied sampling schemes. A numerical method is constructed for finding strategies in suitable classes and for constructing the corresponding control laws. Theorems are proved for the possibility of completing the pursuit by the finite difference method, and they can be used to solve finite-difference optimal control problems or numerical solutions of differential games of fractional order. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.

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