Recurrent Minimization Method in Optimization Problems of Dynamical Systems under Uncertainty

摘要

The "tracking" problem is considered in the deterministic and uncertain case where the initial model of an object that is described by a set of ordinary differential equations is approximately known and the state vector of the object is measured with random errors. The problem considered differs from traditional statements by the fact that a vector-valued function of time that represents the desired output of the object, is given from without at a real-time instant t not on the whole control interval (t_0, T), but only on its "past" part (t_0,t), t_0<=t<=T. In order to solve this problem, the recurrent minimization method is used; this method is based on ideas of imbedding and allows one to reformulate the optimal control problem in terms of the Cauchy problem. The application of the indicated method to the filtration problem and other control problems is considered.