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The paper presents a new method of analyzing large deviations for nonlinear systems defined through matrices with state-dependent coefficients. Large deviations of the controlled process from some standard state is the basis to forecast any critical situation. The task of forecasting is limited to the optimal control problem of Lagrange-Pontryagin optimal control. Two effective methods – State-Dependent Riccati Equations (SDRE) and approximated sequence of Riccati equations (ASRE) – are used. The presented approach to the Lagrange-Pontryagin problem differs from the approach previously used for linear cases by the fact that it uses control in the form of a feedback instead of software open-loop control. This eliminates the need to calculate the end-time boundary value for a conjugate variable, which is the most time-consuming task in nonlinear cases.

Methods of modeling and probabilistic analysis of large deviations of dynamic systems