Method of polynomial predictive control of fail-safe operation of technical systems

In this paper there was obtained a method of the assessment of the probability of fail-safe operation of technical systems in the future instants of time. The method is based on the algorithm for modeling a posteriori nonlinear random sequence of change of values of the controlled parameter which is imposed a limitation of belonging to a certain range of possible values. The probability of fail-safe operations is defined as the ratio of the number of realizations that fell in the allowable range to the total number of them, formed as a result of the numerical experiment. The realization of a posteriori random sequence is an additive mixture of optimal from the point of view of mean-square nonlinear estimate of the future value of the parameter analyzed and of the value of a random variable, which can not be predicted due to the stochastic nature of the parameter. The model of a posteriori random sequence is based on the Pugachev´s canonical expansion. The method offered does not impose any significant constraints on the class of random sequences analyzed (linearity, stationarity, Markov behavior, monotoneness, etc.).