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根据分数阶微积分的相关理论利用自适应滑模控制方法研究分数阶Victor-Carmen混沌系统的滑模同步控制问题,设计分数阶滑模函数并给出控制器的构造,利用Lyapunov稳定性理论给出严格的数学证明,得到系统取得滑模同步的两个充分性条件。研究结果表明:选取适当的控制律以及滑模面下,分数阶Victor-Carmen系统取得混沌同步。数值算例表明该方法有效。
Based on the theory of fractional calculus, the sliding mode synchronization problem of fractional Victor-Carmen chaotic system is studied by using adaptive sliding mode control. The fractional sliding mode function is designed and the controller structure is given. Lyapunov stability theory A rigorous mathematic proof is obtained for two sufficient conditions for the system to achieve sliding mode synchronization. The results show that the chaos synchronization is achieved by choosing the appropriate control law and the fractional Victor-Carmen system under the sliding mode. Numerical examples show that the method is effective.