OPTIMAL CONTROLLING PATH DETERMINATION WITH THE HELP OF HYBRID OPTIONAL FUNCTIONS DISTRIBUTIONS
DOI:
https://doi.org/10.15588/1607-3274-2018-1-17Keywords:
hybrid function, multi-optional control, distribution density, optimal path, variational principle, optimal controlling surface, optional functions entropy.Abstract
Context. The problem of the determination of the optimal value of the augmentation coefficient of a proportional governor includedinto an inertness-less linear object control system on the basis of a synthesized model is solved. The object of the presented study is the
optimal control process.
Objective. The goal of the work is a creation of a method for a problematic situation of the optimum definition, evaluation, and
determination solving at the control system.
Method. A rough model of the phenomenon, and simplified dependence of optimal controlling trajectory upon the cost, of control in
an inertness-less linear controlling system equipped with a proportional governor are proposed. The accuracy of the behavior of the
investigated linear object of control has been chosen in the given consideration as an initial target value which needs to be minimized. The method of the model building with regards to an expenditures principle is offered. It provides taking into account the cost of controlling
process. It allows finding the optimal controlling value on the multi-optional basis. There applied a certain analogue to the subjective
entropy maximum principle of the subjective analysis in order to obtain a specific optimal distributions for the objective value in the view
of the composed functional. The method of the uncertainty degree of the options extremization is improved by a continuous optional value
introduction that allows forming the value distribution density. The optional synthesized model of the control process is built.
Results. The developed theoretical models allow obtaining, and have been implemented in, finding the hybrid optional density as an
optimal solution of a variational problem with two independent variables, which maximal value is the sought optimal controlling path
delivering minimum to the integrated expenses pertaining with the process.
Conclusions. The numerical experiments on the proposed methods studying in the problem of optimization are conducted. The
discovered dependencies are substantiated as a result of these experiments. Their use in practice makes it possible, and is recommended, to carryout optimal control in the described systems. The prospects for further research may include creations of models for the optimal control trajectories findings on conditions involving rates of the considered values varying and in probabilistic, stochastic, undetermined
problem settings.
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