Two-stage approach to solving declaratively set tasks of control a plant with frequency uncertainty by iterative methods

The increasing complexity of control plants leads to a decrease in the degree of their research with an increasing level of unreliability of a priory information, uncertainty in the formulation of tasks for the synthesis of automatic control systems and forces the expansion of the use of approximate mathematical models. As a result, iterative problem solving methods are more widely used, implementing the principle of consistent approximation to the desired result that meets the specified requirements. Iterative algorithms provide for the cyclic execution of a number of operations that implement the iterative method used to solve the problem. Despite the wide range of software development tools, numerous libraries of standard and other various mathematical programs, the designer does not have the opportunity to independently developing the necessary software to solve the problems of control systems design. This is especially important when using iterative problem solving methods, which involve variability in the source data and algorithms with their cyclic application in the problem solving process, which creates additional difficulties. The use of automatic program synthesis is limited by the algorithmic unresolvable of the cyclic program synthesis problem. To solve this problem, a methodology is proposed for applying a two-stage approach to the automatic solution of declarative set tasks using iterative methods, including the automatic construction of an action plan and its subsequent execution in a generated virtual algorithmic structure, including conditions and cycles. The implementation of the approach is based on the planning of actions by a planning artificial neural network and the execution of the constructed action plan into a generated algorithmic structure controlled by the conditions of applicability and requirements for the results of solving the problem. The resolvability of action planning algorithms is shown, which generate a task solution plan in the form of a subset of the axioms of the knowledge model describing the necessary operations to build the desired result. A generalized scheme of cyclic execution of operations of the task solution plan is proposed, controlled by the requirements for the desired result, presented in the form of aggregated operations, including an analysis of the conditions of applicability. The resolvability of the proposed two-stage method is proved. An example illustrating the application of a two-stage method to solve a model problem is considered. Its practical interpretation is shown, including for control tasks of an indefinite plant with multiplicative frequency uncertainty.