Quasipotentials in synthesis of control system based on knowledge

Abstract

The application of the Wentzel-Freidlin asymptotic method in the control problem of estimating the probability of large deviattions is considered. This problem is reduced to the Lagrange optimal control problem for the action functional. In the case when state space matrix of object is Hurwitz matrix, the existence of a unique solution of the Lagrange problem in the form of quasipotential extremals (QE) is established. Based on QE it is possible to build an effective prediction of critical states of control process. The advantage of this method allows arranging the information on the high level, and thereby, building a control system that is based on knowledge. An example of a seaworthiness control algorithm design for a vessel on-board system is shown. In this case, the proposed method of prediction of the critical state based on the action functional leads to frequency-doubling principle known for the Mathieu equation.