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ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 5. Vol. 25. 2019
N. P. Demenkov, Ph. D., Associate Professor, dnp@bmstu.ru, E. A. Mikrin, D. Sc., Professor, evgeny.mikrin@bmstu.ru, I. A. Mochalov, D. Sc., Professor, intelsyst@mail.ru, Moscow, MSTU named after N. E. Bauman
Fuzzy Optimal Control of Linear Systems. Part 1. Positional Control
Single-point boundary tasks are considered in part 1 for the fuzzy nonlinear differential equations like Rikkati and for the fuzzy linear differential equations. The fuzzy nonlinear differential equations arise at the solution of problems of synthesis of optimal linear regulators by method of dynamic programming. The fuzzy linear differential equations appear at synthesis of regulators by criterion of the generalized work. Three types of fuzzy optimization control problems are formulated. The first of these is the problem of synthesizing an optimal fuzzy regulator with full feedback. In the second task, the fuzzy functional of the generalized work is used as the optimality criterion. The third problem is formulated as a fuzzy optimization problem on the maximum principle and with a fuzzy right end. For the first fuzzy optimization problem solved by the dynamic programming method, Buckley-Feuring and Seikkala types of fuzzy optimal control are obtained. An example of optimal control of a DC motor with fuzzy dynamic parameters is considered, and conditions for the existence of Buckley-Feuring and Seikkala types of controls are formulated. For the second optimization problem, a fuzzy partial differential equation is solved, which leads to a fuzzy Cauchy problem for a linear differential equation. By the example of motor control with fuzzy parameters, the absence of a Buckley-Feuring optimal control is shown, however, an optimal Seikkala type controller with full feedback is obtained.
Keywords: Fuzzy boundary value problems, synthesis of fuzzy optimal controllers, fuzzy differential equations, membership function, fuzzy initial problem, fuzzy systems of linear algebraic equations, maximum principle, dynamic programming, criterion of generalized work
P. 259–270