State Estimation of Nonlinear Dynamical Systems on the Basis of Nonquadratic Cost Functions

Abstract

In the present paper, the problem of improving the reliability of state estimation of nonlinear dynamical systems under the conditions of parametric and statistical uncertainty is solved. The solution of this problem is based on the combination of the possibilities of adaptive robust and guaranteeing techniques for signal processing, The proposed technique relies on the theory of multilevel optimization of stochastic systems on the basis of nonclassical cost functions. This technique includes the following: the key parameter is formed for the first level of optimization, which characterizes the accuracy of estimation; the generalized parameter is formed, which characterizes the reliability of estimation; tolerances on the generalized parameter are specified; the likelihood function is formed, which includes the parameters of the first and second levels of optimization; using the maximum principle technique and the method of invariant imbedding, the two-point boundary-value problem is solved. The algorithms synthesized for adaptive robust data processing with guaranteeing tuning from the generalized parameter is shown.