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在参数未知的情况下,对于一个新的超混沌系统,首先设计最优控制器和参数自适应律实现了混沌系统的控制,并根据最优化原理和Lyapunov方法,选取适当的Lyapunov函数,应用Lyapunov第二方法通过推导得到Lyapunov函数关于系统的全导数是恒小于零的,根据Lyapunov稳定性定理,系统在零点是一致渐近稳定的,从而从理论上证明了控制器的有效性,紧接着对两个相同结构的混沌系统,根据最优化原理设计最优控制器和参数自适应律,实现了混沌系统的同步,并应用Lyapunov第二方法从理论上给予了证明,最后通过Matlab软件对控制与同步的效果进行了数值仿真,数值仿真的结果显示同步系统在很短的时间内很快达到了同步,进一步说明了同步方法的正确性与有效性。
For a new hyperchaotic system with unknown parameters, the optimal controller and parameter adaptive law are designed to control the chaotic system. Based on the principle of optimization and Lyapunov method, an appropriate Lyapunov function is selected and Lyapunov The second method derives the Lyapunov function that the total derivative of the system is always less than zero. According to the Lyapunov stability theorem, the system is uniformly asymptotically stable at zero, which proves the validity of the controller theoretically. Then, Two chaotic systems of the same structure are designed according to the optimal principle to design the optimal controller and parameter adaptive law to achieve the synchronization of the chaotic system. The Lyapunov second method is applied to prove the theory. Finally, The results of numerical simulation show that the synchronization system achieves synchronization quickly in a short period of time, further illustrating the correctness and effectiveness of the synchronization method.