ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 6. Vol. 25. 2019

DOI: 10.17587/it.25.323-330

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, MSTU named after N. E. Bauman

Fuzzy Optimal Control of Linear Systems. Part 2. Program Control

When using the maximum principle to find the optimal control, it is necessary to solve a two-point boundary value problem for a system of ordinary differential equations, which is more complex than the initial one. However, in some important cases, for example, when optimizing linear systems with a quadratic functional, the two-point problem can be transformed to the Cauchy problem. Initially, the traditional problem is solved with the transfer of boundary conditions, and then after phasing of the parameters of the problem, the corresponding fuzzy problem is solve. When transferring conditions for a two-point boundary value problem from the left on the right end of the trajectory, the solution consists of the following steps. An initial task is formed on finding vectors of conjugate variables. An initial problem is defined for determining a transferable vector. A system of algebraic equations is solved for the state vector components missing at the right end. The transition to a fuzzy boundary-value problem is performed by fuzzing the elements (parameters) of the matrix for the classical problem and applying the expansion principle to it when its Seikkala and/or Buckley-Feuring solution is obtained using the transition matrix. The example is given.
Keywords: Fuzzy boundary value problems, the optimal synthesis of fuzzy controllers, fuzzy differential equations, membership functions, fuzzy initial problem, maximum principle, dynamic programming, the criterion of the generalized work

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