Parameters identification of nonlinear Lorenz chaotic system for high-precision model reference synchronization

The Lorenz chaotic system synchronization has been a popular research topic in the last two decades. Most of the studies focus on the design of model reference adaptive control (MRAC) synchronization schemes. In the existing MRAC schemes, adaptive laws are designed to estimate the system parameters online. However, due to the system parameters being unknown, arbitrary selection results in a longer estimation period. Although applying large values of adaptive gains can increase the estimation convergence speed, it usually induces obvious estimation oscillations and thereby causes large control efforts. On the contrary, small adaptive gains result in smooth but sluggish transient estimations. None of the studies addressed the importance of parameters estimation for high precise synchronization. To solve this issue, two system identification schemes are presented. The first applied scheme is called the observer/Kalman filter identification (OKID). The second one is called the bilinear transform discretization (BTD). The related detail derivations for the Lorenz chaotic system parameter identification will be presented in this paper. Results show that the proposed BTD identification algorithm is much simpler and computationally efficient. Moreover, highly precise parameter estimations can be achieved as well. Nevertheless, due to the complex nonlinearity of the chaotic system, it will be illustrated that even extremely small parameter deviations could lead to dramatic mismatches for the chaotic system model output prediction. To further solve this issue, a MRAC is further designed in which the initial guess of the system parameters is obtained through the proposed BTD identification algorithm. Based on the contribution of the developed method, the identified parameters are already very close to the true values. As a consequence, applying smaller values of adaptive gains is able to achieve fast convergence of the synchronization of chaos. With the aid of precise parameter identification, the transient dynamics and the convergence performance of the MARC are both improved significantly. Simulations demonstrate the effectiveness of the proposed scheme.