【作者】 张锋；

【导师】 张国山；

【作者基本信息】 天津大学 ， 控制理论与控制工程， 2009， 硕士

【摘要】 基于状态反馈的线性二次型最优控制的研究已经取得了丰硕的成果,但是,在工程实际中,并非所有的状态变量都是能够测取或容易测取的。从工程的角度来看,基于输出反馈的线性二次型次优控制的研究更具有现实意义。因此,越来越多的控制理论学者将研究的重点转移到二次型次优控制问题上来。本文主要研究了基于输出反馈和动态补偿的二次型次优控制问题,提出了一些新的方法和结论,主要内容如下:1基于静态输出反馈研究了线性定常系统、不确定连续系统以及不确定离散系统的LQ次优控制问题,基于线性矩阵不等式给出了次优解存在的充分条件,设计出了次优控制器,得到了次优解。推导过程中没有将静态输出反馈等价为状态反馈,并且不需要假设系统输出矩阵的核为零,因此具有更大的使用范围。数值算例说明了本方法的可行性。2研究了应用动态补偿解决线性二次型次优控制问题,通过等价变换,将补偿器的控制作用等价为增广系统的静态输出反馈控制作用。基于线性矩阵不等式给出次优解存在的充分条件,设计出了动态补偿器,给出了次优解,通过数值算例验证了方法的可行性。3研究了广义系统的二次型次优控制和平均最优控制问题,将在静态输出反馈和动态补偿器作用下的线性定常系统的二次型次优控制问题的结论推广到了广义系统,基于线性矩阵不等式得出了广义系统次优解存在的充分条件,设计出了次优控制器,得出了次优解;针对广义系统平均二次指标的最优控制,通过数学计算,以非线性方程的形式给出了最优控制问题有解的必要条件,设计出了最优控制器,并得到了平均最优解。更多还原

【Abstract】 The study on linear quadratic optimal control based on state feedback has been achieved fruitful results. However, all of the state variables can not be measured or easily measured in engineering practice. The research on linear quadratic suboptimal control based on output feedback is more practical significance in the engineering view- points. The suboptimal control problem has attracted more and more control theorists. This thesis studies the problems of linear quadratic suboptimal control with static or dynamic feedback control. Some new design techniques and results are proposed. The main contents are as follows:1. The problems of the LQ suboptimal control with static output feedback control for linear time-invariant systems, uncertain continuous systems and uncertain discrete- time systems are investigated. A sufficient condition for the existence of solutions for the LQ suboptimal control problems is presented in terms of matrix inequality. The controllers are designed. The results of the LQ suboptimal control are obtained. This approach is more useful because the output feedback needn’t to be equivalent to the state feedback in derivation process and the kernal of output matrix does not demand equal to zero. This approach is turned out to be feasible by the numerical example.2 The problem of the linear quadratic suboptimal with dynamic compensator is discussed. The control with dynamic compensator is equal to the control of the augmented Systems with static output feedback through equivalent transformation. A sufficient condition for the existence of solutions for the LQ suboptimal control problems is presented in terms of matrix inequality. The controller is designed. The results of the LQ suboptimal control are obtained. This approach is turned out to be feasible by the numerical example.3 The problems of LQ suboptimal control and optimal control with average performance criterion for descriptor systems are concerned in this paper. The results of LQ suboptimal control with static output feedback and dynamic compensator for the linear time-invariant systems are extended to the descriptor systems. A sufficient condition for the existence of solutions for the LQ suboptimal control problems is presented respectively in terms of linear matrix inequality. The controllers are designed. The results of the LQ suboptimal control are obtained. A necessary condition in forms of nonlinear equations for the solvability of the optimal control with average performance criterion is worked out for the descriptor systems. The controller is designed. The results of the LQ suboptimal control are obtained.更多还原