Akademik Məlumat İdarəetmə Sistemi
Vestnik Tomskogo Gosudarstvennogo Universiteta - Upravlenie, Vychislitel'naya Tekhnika i Informatika, no.54, pp.4-11, 2021 (ESCI, Scopus)
Consider the following system of fractional order nonlinear difference equations (equation presented) with initial conditions x(t0 ) = x0. (2) Here x(t) is the n-dimensional vector of phase variables, u(t) is the r-dimensional vector of control actions, are given, f(t, x, u) is the given n-dimensional vector function, whose components fi (equation presented) of system (1)-(2) generated by all possible admissible controls, we define the functional S (u) = φ(x(t1 )). (4) Here φ( x) is a given scalar function continuous with φx (x). An admissible control u(t) delivering a minimum to functional (4) under constraints (1)-(3) is called an optimal control, and in this case, a pair (u (t), x(t)) is called an optimal process. In what follows, the minimum problem of functional (4) under constraints (1)-(3) will be called problem (1)-(4). Our goal is to derive the necessary optimality conditions in the problem under consideration.