METHODS FOR CONTROLLING THE RELIABILITY OF COMPUTATIONAL IMPLEMENTATION OF DYNAMIC SYSTEMS MODELS BASED ON THE APPLICATION OF CONTROL ALGORITHMS

Abstract

The paper proposes methods for checking the reliability of computational implementation of mathematical models (MM) of dynamic systems in the processes of their modeling and control. A distinctive feature of these methods is the construction of the latter using control calculation procedures, and the algorithm of control calculations is an integral part of the general algorithm of a particular method. Reliability checking arises due to the need to eliminate failures that, with a high probability, appear when implementing MM of dynamic systems in applied modeling and control problems. Moreover, the relevance of checking the reliability of solving expressions that make up MM of dynamic systems (the essence is the implementation of MM) is due to the inclusion of appropriate computational tools directly in the control loop, and therefore the adequacy of the MM representation directly affects, ultimately, the quality of the control process.The organization of control assumes the presence of reference values with which the results of calculations are compared.In the methods considered in the work, it is proposed to use, as reference values, the controlled results of previous calculations or results, when obtaining which the probability of failure is small. Based on this, it is obvious to organize the implementation of MM of dynamic systems in the processes of their modeling and control with increasing accuracy of calculations, which consists in sequentially obtaining the value of the function (or, in other words, the output signal of the dynamic system, represented by the corresponding MM) at the calculation step with an increasing order of accuracy of the local error. In addition to the method with increasing accuracy, the work proposes extrapolation and interpolation control methods, the fundamental difference of which is the type of information used for control. In the extrapolation method, to increase the reliability of control at the step of the computational process that is being controlled, information that has already been controlled at the previous steps of the computational process is used. The interpolation control method, unlike the extrapolation method, takes into account the change in the solution at the step of the calculations that is being controlled, which allows for indirect control of the selected reference state function. Solving test problems showed the constructiveness of the proposed methods for controlling the reliability of the computational implementation of the MM in cases of their application to real dynamical systems.