不确定连续非线性系统鲁棒混沌反控制

为了实现一类非线性系统的鲁棒混沌反控制,提出非线性不确定系统鲁棒混沌反控制的非线性比例积分微分控制 （NPID）方法.该方法借助微分跟随器和数值微分环节分别提取驱动混沌动态系统和受控系统输出的微分信号，并在此基 础上根据时间加权的误差绝对值积分（ITAE）最小的原则设计非线性比例积分微分控制器，使受控系统的输出能良好地 跟踪驱动混沌系统输出，实现非线性不确定系统的鲁棒混沌反控制.将混沌反控制的适用范围由离散时间系统拓展到连续 时间系统，由参数结构已知的线性稳定系统拓展到参数结构未知的非线性稳定和不稳定系统.分析和仿真结果表明，微分 跟随器和数值微分环节可以对驱动混沌动态系统和受控系统的微分信号进行高精度实时提取，控制策略具有鲁棒性，控 制器的设计具有不受李雅普诺夫指数配置求取困难和微分几何控制器设计计算复杂性的约束.

Chaos robust anti-control of nonlinear continuous systems with uncertainties

In order to realize chaos robust anti-control of a class of nonlinear system with uncertainties,a nonlinear proportional integral differential(NPID) control method was put forward.Differential signals of the driving chaos system and the controlled system were obtained by tracking differentiator and numerical differentiator.NPID controller was constructed with the principle that the integral of time-weighted absolute error(ITAE) was minimum,so that the available differential signals could be used to force the output of controlled system to follow the chaotic trajectory of the given driving system.Using this method,chaos anti-control was not only extended from discrete system to continuous system but also from linear stable continuous system with clear structure and parameters to nonlinear systems with uncertainties of structure and parameters.Analysis and simulation results show that differential signals of the driving chaos system and the controlled system can be obtained precisely,and the suggested controller design method is free of the constraints of Lyapunov exponents allocation which is often difficult to get.