Synthesis of adaptive observer for nonlinear nonstationary systems

Abstract

A new method for the synthesis of adaptive state observation for a class of nonlinear non-stationary systems is proposed. This task is important and fundamental in control theory and is related to both the control problem and the task of monitoring the efficiency of the system operation. The solution to the problem is based on the generalized observer parameter estimation method to obtain the regression equation necessary for estimating the state and parameters of the system. Further, the dynamic regressor expansion and blending method dynamic regressor extension and mixing method is applied to identify the unknown system parameters. The paper proposes a method for estimating the state vector for a nonlinear non-stationary system in which the unknown parameters depend on the state vector under external disturbances. The results obtained are rigorously proved using mathematical theory. Simulation in Matlab/Simulink is performed to demonstrate the effectiveness of the developed algorithm. The mathematical model of the considered objects is a nonlinear system of equations with variable parameters. Compared to previous methods, the method proposed in this paper is more general, especially in a system where the unknown parameters depend on the state vector with nonlinear functions. However, the problem is currently solved only for discrete systems. In the future, it may be possible to extend it to continuous systems.