Scientific journal
Scientific Review. Technical science
ISSN 2500-0799
ПИ №ФС77-57440

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VARIATIONAL GENETIC ALGORITHM TO SOLVE OPTIMAL CONTROL PROBLEM

Diveev A.I. 1 Shmalko E.Y. 1
1 Institution of Russian Academy of Science Dorodnicyn Computing Centre of RAS
A new numerical method is proposed to solve a multiobjective optimal control problem. According to this approach one basic solution is defined among the finite number of controls in the discrete moments. A set of small variations of this basic solution is constructed. Each variation in the proposed algorithm is defined by a vector of three components. The first one indicates the number of variation point or the moment when the variation is to be done. The second component indicates the value which the basic solution is to be changed on. The third component indicates the number of neighbouring points where the small variation of the basic solution is in inverse proportion to the distance to the variation point. A genetic algorithm searches a solution on the set of small variations of the basic solution. The variational genetic algorithm versus its classic approach reduces the search space of an optimal solution by defining a basic solution and lowers the search time by using vectors of variations of a small size. A numerical example of solving an optimal control problem for well-known nonlinear Duffing system is presented to illustrate the efficiency of the developed method.