A Combined Input-state Feedback Linearization Scheme and Independent Component Analysis Filter for the Control of Chaotic Systems with Significant Measurement Noise

Abstract

Chaotic motion is an undesirable phenomenon in many engineering applications since it leads to a significant degradation of the system performance and restricts the feasible operational range. Therefore, the problem of controlling or suppressing chaos has attracted considerable attention in the literature. However, most chaos control schemes utilize a state feedback signal, and are therefore sensitive to measurement noise. Therefore, a requirement exists for filtering systems capable of separating the measurement noise from the chaotic signal in order to improve the performance of the controlled system. However, the chaotic signal and the measurement noise are both broadband signals, and thus the measurement noise can not be filtered using a low-pass filter since this causes a distortion of the chaotic signal. Accordingly, this paper presents a control scheme for chaotic dynamic systems with significant measurement noise featuring an input-state linearization scheme and a filter based upon an independent component analysis algorithm. The feasibility and effectiveness of the proposed approach are demonstrated by way of numerical simulations using a general Lorenz system for illustration purposes.