Numerical computations of the safe boundaries of complex technical systems and practical stability

Abstract

In this article we discuss methods of computing the guaranteed values of the states of a technical system in order to estimate the safety of a technical system The danger of a system functioning is a threat, possibility, probability of damage, system catastrophe, that is, potential damage to a technical system in certain conditions and situations. An analysis of the boundaries of the safety areas of technical systems helps to obtain quantitative estimates of the possibility of dangerous situations. The presence of such estimates may allow a more reasonable search and development of a set of measures to eliminate or mitigate the consequences of such situations. The article discusses the new results of computing the guaranteed boundaries of solution sets and the results of their application for assessing the boundaries of security areas and studying practical stability. Methods are used based on the approximation of the shift operator along the trajectory, and taking into account the influence of constantly acting perturbations on the solutions.