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借助于Chebyshev多项式近似,考察了随机参数服从拱形分布的一个电路系统的混沌控制。首先,用正交多项式逼近原理将一个随机振荡电路系统转化成与其等价的确定性系统,这样得到的系统是与原系统在均方残差为极小意义下的一种加权平均近似。其次,设计了带有微分项的非线性反馈控制器,根据受控系统的分岔参数图通过调节控制强度k,找到并且控制到此系统的非稳定周期轨道上。数值结果表明。所用方法是有效可行的。
With the help of the Chebyshev polynomial approximation, the chaotic control of a circuit system with random parameters obeying the arcuate distribution was investigated. First of all, by using the principle of orthogonal polynomial approximation, a stochastic oscillating circuit system is transformed into its equivalent deterministic system. The resulting system is a weighted average approximation of the mean square error of the original system. Secondly, a nonlinear feedback controller with differential term is designed. According to the bifurcation parameter map of the controlled system, the control strength k is found and controlled to the unstable periodic orbit of this system. Numerical results show. The method used is effective and feasible.