OPTIMAL DISCRETE CONTROL SYNTHESIS RESEARCH

The article deals with the issues of synthesis of a discrete control system for multidimensional dynamic objects using the methods of graph theory and calculus of variations. As a criterion for the quality of the control system, minimization of the total squares of the deviation of the values of the variables from the given one was taken. The calculation of transient processes is carried out with a hybrid use of topological and interpolation methods. Accounting for the delay property of the control objects is provided by discarding zero elements from the generated matrix of coefficients. The optimal control, formed for the synthesis of the control device, is defined as a function of the deviation of the output variables from the reference and previous control actions. This representation of the functioning of the control device allows you to fully take into account the dynamics of the controlled system in the development of control actions and is distinguished by the convenience of implementation in the microcontroller. The described control synthesis approach is convenient in that it is enough to have an object model in the form of a transition function, which is relatively easy to obtain as a result of active or pseudo-active experiments on the object, or as a result of statistical processing of data collected in a passive way. The analysis of the obtained results showed the adequacy of the solutions, but the latter is distinguished by convenience and speed.

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