一类含Lipschitz非线性的广义离散系统的预见控制

Preview control for a class of descriptor discrete-time systems with Lipschitz nonlinearities

研究一类含有Lipschitz非线性项的广义离散系统的预见控制.首先,采用一阶前向差分算子,对原广义系统的状态方程进行差分运算,从而得到了一个包含跟踪误差信号的广义增广误差系统;其次,对广义增广误差系统设计一个状态反馈控制器.由Lyapunov稳定性理论,设计出一个使得闭环系统渐近稳定的充分条件,从而得到了原广义系统的一个预见控制器,使得其输出信号实现了对参考信号稳态、无差地跟踪.最后,一个数值算例证明了该方法的有效性.

This paper studies the preview control of a class of descriptor discrete-time systems with Lipschitz nonlinear terms.Firstly,the state equation of the original system is calculated by the first order forward difference operator,and an extended error system is obtained,in which the tracking error,reference signal and interference signal are considered.Secondly,a state feedback controller is designed for the established extended error system.Based on the Lyapunov stability theory,a required condition for ensuring the asymptotic stability of the system is proposed.Thus,we obtain the predictive controller of the original system,so that the system output can achieve steady-state and error-free tracking of the reference signal.Finally,a numerical example proves the effectiveness of this method.