Abstract
The paper presents a new method of large deviations analysis for nonlinear systems in the form of state-dependent coefficients. The large deviations of the controlled process from some regular state is the basis of forecasting of the critical situation. The forecasting problem is reduced to the Lagrange-Pontryagin optimal control problem. The presented approach to state-dependent coefficients for the solution of Lagrange-Pontryagin problem is different from the approach used before for linear cases in the fact that it uses a control in the form of feedback instead of programmable control. This eliminates the need to calculate the boundary value in the final time point for the conjugate variable, which is the most time-consuming task in nonlinear cases. An example of using the presented approach to the problem of vessel tilting prediction is considered.
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