About One Generalization of the Classical Physics Problem of Controlled Inverted Pendulum
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A problem of a couple of connected inverted pendulums is considered under stochastic perturbations of the type of the Wiener and Poisson processes. This problem generalizes the classical physics problem of a controlled inverted pendulum and continues a series of unsolved problems in stability and optimal control theory for stochastic delay differential equations, published by the author from 2010 to the present. Since none of these problems has been solved yet, the purpose of this paper is to attract the attention of interested researchers to these problems, which may lead both to the solution of at least some of them and to the general development of stability and optimal control theory for stochastic systems.
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