Parameter Identification of Chaotic Systems Using a Modified Cost Function Including Static and Dynamic Information of Attractors in the State Space

Parameter identification (PI) is very important in system analysis and controller design and has wide applications in industry. PI is an essential step in designing mathematical models of the dynamical systems based on the measured data. Identification of chaotic systems is very challenging due to the butterfly effect. Recently, a state-space-based cost function based on Gaussian mixture model (GMM) has been proposed for the PI of the chaotic systems. In there, a GMM as a statistical model of the measured data modeled static features of the chaotic attractors in the state space. In this paper, we propose a new method which incorporates static and dynamic features in the GMM modeling in order to achieve a better cost function for the PI problem. The proposed method can extract suitable information from the trajectory of the chaotic attractor. We conduct some experiments for one-dimensional PI. Using measured data from 4D and 3D chaotic systems, empirical results indicate success of the proposed method.