Open AccessOptimisation problem for some class of hybrid differential-difference systems with delay
Author(s) -
M. Dymkov
Publication year - 2021
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2021-1-6-17
Subject(s) - hyperplane , mathematics , differential (mechanical device) , optimal control , class (philosophy) , state (computer science) , control theory (sociology) , function (biology) , trajectory , regular polygon , mathematical optimization , zero (linguistics) , control function , control (management) , computer science , algorithm , linguistics , philosophy , physics , geometry , artificial intelligence , evolutionary biology , engineering , biology , aerospace engineering , astronomy
In the paper, the linear differential-difference dynamic systems with delayed arguments are considered. Such systems have a lot of application areas, in particular, processes with repetitive and learning structure. We apply the method of the separation hyperplane theorem for convex sets to establish optimality conditions for the control function to drive the trajectory to zero equilibrium state in the fastest possible way. For the special case of the integral control constraints, the proposed method is detailed to establish an analytical form of the optimal control function. The illustrative example is given to demonstrate the obtained results with the step-by-step calculation of the basic elements of the optimal control.