不确定离散时间系统的鲁棒预见控制

发布时间：2018-03-21 04:23

本文选题：不确定离散系统　切入点：预见控制　出处：《北京科技大学》2017年博士论文　论文类型：学位论文

【摘要】：确定性系统的预见控制理论的研究已经取得了很大的进展.然而对预见控制系统,不可避免地会存在某些不确定性,因此将预见控制理论和不确定系统相结合,研究鲁棒预见控制问题就自然地成为一个新的课题.本文主要作了以下几方面的研究工作:1.研究了范数有界不确定性的离散时间系统鲁棒预见控制问题.为了克服经典的差分方法无法推广到不确定系统中的困难,本文采用一种辅助方法构造扩大误差系统.然后利用线性矩阵不等式(LMI)技巧将增益矩阵的求解问题转换为一个凸优化问题,分解代回原系统便得到预见控制器.2.研究了变时滞不确定离散时间系统的鲁棒预见控制问题.首先利用模型变换的方法将系统中的变时滞项连同不确定项从形式上提取出来,并将上述的构造方法推广过来.然后运用标度小增益定理给出预见控制器的设计方法.最后数值仿真表明预见控制器的优越性.3.考虑了一类参数不确定离散时间系统的参数依赖的预见控制器设计问题.将经典的差分方法运用到不确定离散时间系统中,构造出包含未来目标值信号的信息的扩大误差系统,将跟踪问题转化为调节问题;然后结合LMI的方法和参数依赖的思想,设计了参数依赖预见控制器.4.研究了时变参数不确定离散时间系统的鲁棒预见控制.首先利用辅助变量的构造方法和状态增广技术推导出扩大误差系统.然后利用参数依赖的Lyapunov稳定性理论和LMI方法,得到了保证闭环系统渐近稳定的充分条件.接着,通过求解有限个线性不等式,得到预见控制器的增益矩阵.5.研究了不确定离散时间系统的输出反馈预见控制问题.首先构造出不确定离散时间系统的扩大误差系统;然后针对扩大误差系统,改写输出方程,使得充分利用可预见信号的信息.最后利用鲁棒控制的有关理论方法求解出输出反馈增益矩阵.上述所有的情况都对定理成立的条件给出了严格的数学证明.
[Abstract]:Great progress has been made in the study of predictive control theory for deterministic systems. However, some uncertainties inevitably exist in the predictive control systems, so the theory of predictive control is combined with uncertain systems. The study of robust foresight control problem has naturally become a new subject. In this paper, the following research work is done: 1. The problem of robust predictive control for discrete-time systems with norm-bounded uncertainties is studied in order to solve the problem of robust foresight control in discrete-time systems with norm-bounded uncertainties. The classical difference method can not be extended to the difficulties of uncertain systems. In this paper, an auxiliary method is used to construct the extended error system, and then the problem of solving the gain matrix is transformed into a convex optimization problem by using the LMI (linear matrix inequality) technique. The problem of robust predictive control for uncertain discrete-time systems with variable time-delay is studied. Firstly, the variable time-delay term and the uncertain term in the system are extracted from the formal form by the method of model transformation. Then the design method of the predictive controller is given by using the scalar small gain theorem. Finally, the numerical simulation shows the superiority of the predictive controller. 3. A class of parameter uncertain discrete time is considered. The classical difference method is applied to uncertain discrete-time systems. An extended error system containing the information of the future target signal is constructed, and the tracking problem is transformed into an adjustment problem, and then the method of LMI and the idea of parameter dependence are combined. A parameter-dependent predictive controller .4.The robust predictive control for time-varying uncertain discrete-time systems is studied. Firstly, the extended error system is derived by using the construction method of auxiliary variables and the state augmentation technique. Using parameter-dependent Lyapunov stability theory and LMI method, Sufficient conditions for the asymptotic stability of closed-loop systems are obtained. Then, by solving finite linear inequalities, The gain matrix of the predictive controller is obtained. 5. The output feedback foresight control problem of uncertain discrete time system is studied. Firstly, the extended error system of uncertain discrete time system is constructed, and then the output equation is rewritten for the extended error system. Finally, the output feedback gain matrix is solved by using the theory of robust control. All the above cases give strict mathematical proof for the condition that the theorem holds.
【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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