On multiextremality in the estimation problems of deterministic chaos systems

The nonlinear dynamic systems used for the modeling of some processes or remainders when using linear models are considered. The problem of state estimation (as well as parametric identification) on the basis of maximum likelihood method is formulated. To solve the problem it is proposed to use homogeneous algorithms of global optimization. The main theorems about the linear type of criterion for homogeneous algorithms of global optimization and about the sufficient condition of convergence of homogeneous algorithm of global optimization are given. The results of state estimation for one-dimensional dynamic nonlinear system are given.