Parameter Identification of Chaotic System in Finite-Time Without Persistence of Excitation

Abstract

Chaotic systems are nonlinear deterministic systems that reveal complex and unpredictable behavior. Chaos theory has been exploited for analysis and synthesis in several academic and technical domains, including communication, economic systems, electrical systems, chemical processes, and optimization. A crucial step in analyzing the behavior of a complex system is identifying the chaotic system's parameters. The problem of parameter estimation of the chaotic system is identified and a solution via finite-time estimator has been proposed without the hypothesis that the regressor is persistently excited. As a finite-time estimator, the I-DREM approach is explored to estimate the parameters of uncertain chaotic systems. This paper analyzes the chaotic systems parameter estimation problem under both PE and non-PE conditions for comparison purposes. Additionally, the Lorenz system's unknown parameters are all identified. Finally, numerical simulation results are displayed to show exactly how well the proposed strategy performs.