### Mathematical modeling of increasing the level of safety in case of failures of space technology

Boris Melnikov, Elizaveta Davydova

#### Abstract

As space programs become more sophisticated, the issues of crew safety become more urgent. Due to the extremely high cost of creating and operating manned spacecraft, the cost of losses in case of accidents and failures of aviation and rocket and space technology, and also due to the considerable cost of designing future manned spacecraft, a new approach to ensuring the safety of people at the launch site. For these purposes, we propose to use the mathematical model developed by us to improve the level of safety in the event of an emergency.
In this paper, we propose a new approach to the formulation of optimization problems intended for simulation of emergency situations. This approach can be briefly described as follows. There are some states in which the simulated technique can be located, and for states we also consider the finite sequences of their switching. Examples of such switching are missile launch, launch cancelation, command to the preliminary stage of traction, etc., and each switching is a transition from one state to another. In this case, there is a possibility that some switching will lead to an accident, we consider all such probabilities given.
The coefficients of the matrices are the logarithms of the probabilities that switching between pairs of states does not lead to an accident. In this case, each sequence of states, i.e., some sequence of switching, gives a logarithm of the general probability of absence of an accident. The model we are considering uses the widely known problem of discrete optimization - namely, the traveling salesman problem. We are striving to ensure that the likelihood of an absence of an accident corresponding to some sequence of switchings would be minimal. Since the traveling salesman problem is difficult to solve, we are usually satisfied with finding some pseudo-optimal solution, which, as we believe, corresponds to a sequence of switches that is reasonably close to optimal.

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