摘要:
本论文研究了具有随机扰动和未知参数的Lorenz混沌系统,其中随机扰动是一维标准Wiener随机过程.基于随机李雅普洛夫稳定性理论、It?o (伊藤)公式以及自适应控制方法,本文分别通过设置三个和两个控制器,从理论上提出了两个均方渐近自适应同步标准,这些标准简单易行,不仅能使得随机扰动下的驱动系统和响应系统达到均方渐近同步,而且能同时识别出系统中的未知参数.最后的Matlab数值模拟验证了提出的理论结果的正确性和有效性.
Abstract:
In this paper, Lorenz chaotic system with stochastic perturbation and unknown parameters is investigated, in which the stochastic perturbations is one-dimensional random process of the standard Wiener. Based on stochastic Lyapunov stability theory, It?o formula and adaptive control method combined with three adaptive control laws and two adaptive control laws respectively, two mean square Asymptotic adaptive synchronization standards are put forward theoretically. These new standards are in a simple form and easy to deal with. Moreover, with these standards, not only drive system with stochastic perturbations can be synchronized with the respond system, but also unknown parameters in the system can be identified. Finally, the Matlab numerical simulations confirm that the proposed results are correct and effective.
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