滑模控制的多混沌系统组合函数投影同步

Combined Function Projection Synchronization of Multi-chaotic Systems Based on Sliding Mode Control

将函数投影同步和组合同步方法相结合,研究了两个混沌驱动系统和多个混沌响应系统之间的组合函数投影同步问题。基于李雅普诺夫稳定性定理和滑模控制方法,设计了相应的滑模面和控制器,通过设计切换面和控制律,使误差系统的运动轨迹沿滑模面滑动并最终趋于稳定。该组合同步方式中,混沌驱动系统和混沌响应系统可以扩展为3个或者多个混沌系统,同步方式具有一定的通用性。控制器的设计考虑了外部干扰和抖振的影响,具有一定的鲁棒性。数值仿真结果表明:驱动系统与响应系统按照函数比例因子m(t)实现同步,同步误差e收敛于0,验证了该设计方法的可行性和正确性。

Based on function projection synchronization and combined synchronization method,the combined function projection synchronization between two chaotic drive systems and multiple chaotic response systems was studied.The corresponding sliding surface and controller were designed based on Lyapunov stability theory and sliding mode control method.The designed switching surface and control law made the motion path of the error system slide along the sliding surface and finally stabilize. The chaotic drive system and the chaotic response system in the combined synchronization method were extended into three or more chaotic system,with certain versatility. The design of the controller took into account the effects of external disturbances and chattering and had robust. The numerical simulation results show that the driving system and the response system realize synchronizationin accordance with the function scale factor m(t),and the synchronization error e converges to 0,which verifies the feasibility and correctness of the design method.