Abstract: A general strategy is developed for controlling the chaos in the distributed parameter sysytems without underlying model equations．The Karhunen-Loeve procedure is utilized to decompose the spatiotemporal pattems in the system and identify the dominant spatial modes with the first return mapping in the Poincare section to obtain the setpoint.The linear feedback on the deviation of dominant spatial structure between the setpoint and the measured one is used to stabilize the system.A non-isothermal catalytic reactor undergoing period-doubling and an isothermal bioreactor undergoing quasiperiod-doubling are taken as two examples and the performance of the proposed strategy is demonstrated via numerical simulation.The simulation results illustrate that this methodology works satisfactorily and the system can be stabilized into period-one.The controlled dynamics is indeed the embedding unstable periodone orbit for the period-doubling chaotic system while some offsets between the controlled dynamics and setpoint are existing for the quasiperiod-doubling chaotic system.

摘要： 提出了分布参数系统中混沌行为控制的方法．这一方法只要求过程的动态测量值而不要求关于过程的数学模型．首先，利用Karhunen-Loeve法即特征主元分析法把分布参数系统中混沌的时空模式分解为不随时间变化的空间模式和随时间变化的时序系数．随后，在Poincare截面上应用首回映射确定具有主要能量的特征空间模式的控制设定值．最后，运用负反馈策略和“系统松弛”技术控制混沌系统．以两个模拟反应器为例，考察了化工过程中由扩散引起的分别由两类不同途径产生的混沌行为的控制．仿真结果表明，该方法能镇定混沌系统而变为一周期系统．对于周期倍增系统，控制得到的被稳定周期即为混沌吸引子中所期望的不稳定一周期；而对于准周期倍增系统，则存在一定的偏差．