不确定离散时间系统的有限时间预见跟踪控制

Finite-time preview tracking control for uncertain discrete-time systems

研究一类不确定离散时间系统的有限时间鲁棒预见控制问题.与以往对误差信号和系统方程取差分不同,通过引入辅助变量,并用系统状态向量及输入向量与相应辅助变量之差代替通常的状态差分,避免对时变的系数矩阵取差分,使得扩大误差系统的构造成为可能.另外,所推导的扩大误差系统不再包含误差向量,这不仅能降低系统的阶数而且能推广适用对象.针对所求得的不确定系统的扩大误差系统,分别引入状态反馈和静态输出反馈,并利用Lyapunov函数方法导出闭环系统渐近稳定的充分条件,该条件可以通过求解一个LMI问题而实现.所得控制器回到原系统即可得到带有预见作用的预见控制器.数值仿真验证了研究结果的有效性.

The problem of finite-time robust preview control is proposed for a class of uncertain discrete-time systems.It is different from the difference of error signals and system equations.By introducing auxiliary variables,we use the difference between the system state variables,input variables,and the corresponding auxiliary variables,instead of the usual difference between system states,which makes it possible to construct an augmented error system.In addition,the augmented error system derived no longer contains error vectors,which not only reduces the order of the system,but also extends the applicable object.For the augmented error system,the state feedback and output feedback are introduced,receptively,and based on the Lyapunov stability theory,sufficient conditions are derived for the robust asymptotic stability of the closed-loop systems.The conditions can be realized by solving an LMI problem.The controller returns to the original system,and the preview controller is obtained.The numerical simulation examples also illustrate the effectiveness of the results.