离散时间线性系统有限时间模型预测控制研究

发布时间：2018-04-05 19:05

  本文选题：离散时间线性系统　切入点：有限时间稳定　出处：《鲁东大学》2017年硕士论文

【摘要】：有限时间稳定是系统在受到初始扰动后,在所给定的时间区间内系统的状态不会超出规定的误差范围.其问题主要集中在稳定性分析和控制器设计方面.模型预测控制(Model predictive control,MPC)能够有效处理系统约束和参数不确定性等因素,能够使系统有更好的性能,已经成为应用较为广泛的现代控制策略.本文以离散时间线性系统为研究对象,对有限时间稳定预测控制进行了一些研究,总结如下:针对离散时间线性时不变(Linear Time Invariant,LTI)系统研究其有限时间MPC问题.当系统状态不可测时,构造多Lyapunov函数,在有限时域最小化性能指标下,将求解有限时域的最小化转化为具有LMI约束优化问题.利用LMI方法,求解出有限时间稳定输出反馈预测控制器系数矩阵,进而得到动态输出反馈预测控制器.设计出具有有限时间稳定性的预测控制算法.证明了优化问题在所给定的条件下,系统是有限时间稳定的.针对时不变、有限能量外部干扰的LTI系统,研究了有限时间H_∞预测控制问题.给出了线性系统有限时间预测控制的定义,通过构造Lyapunov-Krasovskii函数并结合矩阵不等式技术,得到系统有限时间预测控制器有解的充分条件;进一步,将问题转化为具有线性矩阵不等式约束的优化问题,并给出了相应的求解算法.数值算例和仿真对比图表明了设计方法的有效性.
[Abstract]:Finite time stability is that the state of the system does not exceed the prescribed error range in the given time interval after the system is initially disturbed.The problems mainly focus on stability analysis and controller design.Model predictive control (MPC), which can effectively deal with system constraints and parameter uncertainties, can make the system have better performance, and has become a widely used modern control strategy.In this paper, the finite time stability predictive control is studied for discrete time linear systems. The results are summarized as follows: the finite time Time problem is studied for discrete-time linear time invariant linear Time (LTI) systems.When the state of the system is unmeasurable, multiple Lyapunov functions are constructed, and the minimization of the finite time domain is transformed into an optimization problem with LMI constraints under the finite time domain minimization performance index.The coefficient matrix of the finite time stable output feedback predictive controller is solved by using the LMI method, and then the dynamic output feedback predictive controller is obtained.A predictive control algorithm with finite time stability is designed.It is proved that the optimization problem is finite time stable under the given conditions.For LTI systems with time-invariant and finite energy external disturbances, the finite time H _ 鈭，

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