基于自适应滑模控制的不同维分数阶混沌系统的同步

摘要

针对异结构不同维分数阶混沌系统的广义同步问题进行研究，设计了一种将滑模变结构理论和自适应控制理论相结合的方法。通过设计一种对外界干扰具有强鲁棒性的分数阶滑模面，以及构造合适的自适应滑模控制器，该控制器将系统的运动控制到滑模面上，使系统轨道沿滑动模运动到所需的控制状态，最终实现了两个不同维异结构混沌系统之间的广义同步。以四维超混沌Chen系统和三维Chen混沌系统为例，对这两个系统分别进行升维和降维的同步仿真。仿真模拟结果表明，运用本文设计的控制器，经过短暂的时间，两系统的广义误差变量始终平稳地趋于零，即证明了这种控制器的有效性。%In this paper, based on sliding mode control and adaptive control theory, the synchronization of two different fractional order chaotic systems is investigated. First, a fractional sliding surface with strong robustness is designed and a suitable adaptive sliding controller is constructed, then the error states of the systems are controlled to the sliding surface via the method to guarantee the synchronized behaviors between two fractional chaotic systems. Numerical simulations on the hyper Chen chaotic systems and Chen chaotic system are also carried out respectively. Simulation results show that the generalized errors tend to zero after a short time, and the effectiveness and feasibility of this method are well verified.