Failure-preventing control for multistable structures

The problem of control against escape from a safe region covers a wide range of applications. In this paper we consider mechanical interpretation of this problem for multistable mechanical systems. We suppose that the prescribed operation domain corresponds to a neighbourhood of a fixed stable position, the escape out of this domain is associated with the failure of the system. In this case, the goal of the control is to minimize the probability of leaving a fixed operation domain. For many engineering applications, the problem of escape from a preferred region associated with escape from a potential well. The paper discusses the effect of small random perturbations on escape phenomena in a bistable system and explores optimal control feasibility for such systems.