具有非匹配扰动的非线性变参数系统模型参考跟踪控制

Model reference tracking control for nonlinear parameter-varyingsystems with mismatched disturbances

本文研究了一类含有非匹配扰动的非线性变参数系统的跟踪控制问题.首先,设计非线性扰动观测器用于估计系统所受到的未知扰动.其次,在前馈–反馈跟踪控制器中引入扰动补偿控制项,提出一种基于扰动观测器的跟踪控制策略.利用依赖于状态和时变参数的线性矩阵不等式,导出保证闭环系统输入–状态稳定的充分条件,进而运用平方和凸优化技术解析地构造出扰动观测器和跟踪控制器.通过理论证明,所设计的控制策略能够实现非线性变参数系统输出对参考模型输出的跟踪,消除输出通道中非匹配扰动的影响.最后,由数值仿真例子验证了所提方法的有效性.

In this paper,a tracking control problem is considered for a class of nonlinear parameter-varying systems with mismatched disturbances.First,a nonlinear disturbance observer is designed to estimate the unknown disturbances.Second,a disturbance observer-based tracking control strategy is proposed by introducing a disturbance compensation control item into the feedforward-feedback tracking controller.And utilizing linear matrix inequalities dependent on states and time-varying parameters,the sufficient condition of the input-to-state stability is derived for the closed-loop system.Then the corresponding disturbance observer and the tracking controller are analytically constructed via the sum of squares convex optimization technique.It is proved theoretically that the presented control strategy can make the output of the nonlinear parameter-varying system track the output of the reference model,and eliminate the influence of the mismatched disturbances on the output channel.Finally,a numerical simulation example is given to verify the validity of the proposed method.