一类时变时滞混沌系统的参数辨识方法

A method of identifying parameters of a time-varying time-delay chaotic system

时变的未知时滞参数普遍存在于混沌系统中,它使得混沌系统同步控制变得非常困难.针对时滞混沌系统中参数时变且未知的问题,提出了一种新颖的辨识方法.该方法首先将未知时变参数用分段常数函数来近似,把求解非线性函数的问题转化为参数向量选择问题,其中分段常数函数的高度向量成为待求解参数向量;然后推导了目标函数对分段常数高度向量的梯度信息,结合序列二次规划法求解得最优分段函数;随着分段数的增加,最优分段函数将逼近原非线性时变函数.数值实例结果验证了该方法的有效性.

Unknown time-varying parameters, including time-delay and system parameters, commonly exist in chaotic systems.These unknown parameters increase the difficulties in controlling the chaotic systems, and make most of the existing control methods fail to be applied. However, if these parameters can be estimated, they will facilitate the controller design. Therefore, in this paper, a parameter identification problem for a general time-delay chaotic system with unknown and time-varying parameters is considered, where these unknown time-delay and parameters are slow timevarying. It is very difficult to solve this problem analytically. Thus, a unified identification method is proposed to solve the identification problem numerically. To solve this identification problem, firstly, the time horizon is divided into several subintervals evenly. Then the time-varying parameters are approximated by piecewise constant functions. The height vectors of the piecewise constant functions are unknown and to be determined. Furthermore, the heights of the piecewise constant functions keep constant between each pair of the successive partition time points but switch values at the partition time points. After the approximation, the original identification problem for finding the nonlinear functions of the unknown parameters is transformed into a problem of selecting approximate parameter vectors, where the heights of the piecewise constan functions are unknown parameter vectors to be determined. Secondly, to solve the problem of selecting approximate parameter vectors quickly, the partial gradients of the objective function with respect to the parameter vectors are derived; and they are then integrated with a gradient-based procedure to obtain the unknown heights. As the number of partitions for the piecewise function increases, the optimal results of the approximate problem will approach to the optimal results of the original parameter identification problem. Hence, the optimal piecewise functions will approach to the real nonlinear functions for the unknown parameters. Finally, parameter identification experiments on time-delayed Mackey-Class and time-delayed logistic chaotic systems are carried out. The effects of the partition number on the estimated results are discussed. Numerical results demonstrate that when some switching times of the unknown parameters do not coincide with any partition time points, small error between the estimated results and the real values are present. However, these errors can be filtered and the estimated results are consistent well with the real values. Hence, the proposed method is reasonable and effective.