Abstract
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 large control efforts. On the contrary, small adaptive gains result in smooth but sluggish transient estimations. None of the studies addressed on the parameters estimation and its contribution to precise synchronization. To address this issue, two system identification schemes are presented. The first applied scheme is called observer/Kalman filter identification (OKID). The second one is called 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 relatively simple 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 mismatch 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. Since the identified parameters are already very close to the true value, smaller values of adaptive gains can be used. With the aid of the 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.
Adaptive synchronization and parameter identification for Lorenz chaotic system with stochastic perturbations
