The research of systems with incomplete information in complex control object

Abstract

The article deals with the development of mathematical methods and setting optimal management tasks for the system with variable coefficients that takes into account an apriori incomplete information due to the presence of unobservable coordinates and small parameters. In recent years, the researchers have developed the idea of the possibility of solving the problem without simplification involving certain numerical methods and using modern computational tools. According to the recent studies, one of these methods is the method of singular perturbations. Presently, researchers are interested in studying the issue of allocation of class of systems, for which it is possible to use the method of singular perturbation and to study the structural features of such systems. Among other control systems, the research distinguishes a large class of systems that are experiencing partial movements with varying degrees of intensity of so-called multi-rate transients. Such systems include complex technological systems such as mine — concentrator — metallurgical plant, steel works, and similar sites. The processes in these systems are characterized by a variety of direct, inverse, and cross-linking connections with a significantly differing speed of the flow of technological processes. This paper discusses the multi-rate systems with a variable structure, where it is possible to use the so-called sliding regimes that reinforce the “rude” regulator in their relation to the variations in the parameters of the object. To solve this class of problems, researchers use approximate analytical calculations based on the singular perturbation method. In a case where some of the coordinates of a dynamic system are not observed, the equations of motion are reduced to a system of singularly perturbed equations through artificial introduction of a small parameter. This paper is a summary of the study of the multi-rate system with a variable structure in a case where the equations of motion have variable coefficients.