【作者】 董学平；

【导师】 王执铨；

【作者基本信息】 南京理工大学 ， 控制科学与工程， 2007， 博士

【摘要】 本文的主要研究内容是:运用算子半群理论,讨论一类分布参数混合系统的稳定性、一类分布参数切换系统的稳定性和镇定问题,以及运用广义正交多项式对分布参数系统的有关控制问题进行逼近求解。论文的主要工作及创新点如下:首先,建立了一般分布参数混合系统模型,运用混合动态系统的五元组分析法及其相关理论研究系统的稳定性问题,得出了系统稳定性判别的方法。其次,研究了含指数稳定子系统所组成的分布参数切换系统的稳定性问题。对分布参数切换系统的稳定性进行分析,讨论了一般分布参数线性切换系统的状态反馈镇定问题,对一类分布参数线性切换系统进行了观测器设计,给出了系统动态输出反馈可镇定的充分条件,并且以系统状态的观测值为依据设计了子控制器及切换律,使得系统渐近稳定。对状态反馈镇定和输出反馈可镇定,都讨论了切换时间间隔受限制的情况,并给出了相应的可镇定条件和镇定控制方案。此外,针对切换系统中广泛存在的脉冲效应,提出分布参数脉冲切换系统的模型。讨论了分布参数脉冲切换系统的稳定性问题。同时,对含非线性扰动项和不确定项的分布参数脉冲切换系统的稳定性问题也进行了研究。最后,研究分布参数系统的有限维逼近问题,给出了广义正交多项式的运算法则和逼近法则,并且论证了其在L~2[a,b]空间上的收敛性。将其运用于分布参数系统的最优控制和预测控制问题的逼近求解中,仿真结果表明了方法的有效性。对分布参数切换系统仿真研究过程中,切换律难以求解的问题,运用该方法能够方便地求出逼近切换律,进而完成仿真过程。为分布参数切换系统仿真研究提供了一条有效途径。本文对主要的结论均进行了仿真研究,结果表明:本文提出的设计方案具有良好的效果。更多还原

【Abstract】 By semigroup theory and general orthogonal polynomials (GOP), the stability of a class of distributed parameter hybrid systems (DPHS) and a class of distributed parameter switched systems (DPSS), the stabilization for a class of DPSS and the approximate analysis for distributed parameter control systems were discussed in this dissertation.The chief work and innovation in this paper are as follows:Firstly, a general model for DPHS was established and it’s stability was analyzed using the quintuple analysis method of hybrid dynamical systems and it’s relative theory.Secondly, the stability analysis for DPSS was given. The stability DPSS include exponential stable sub-systems was discussed, and the state feedback stabilization is also presented. In the next place, an observer is designed for a class of DPSS whose sub-system is linear, and a sufficient condition for the stabilization of closed-loop system is also presented. Based on these, a switching strategy and sub-controller, which use the observer value, are designed to guarantee the closed-loop system is exponentially asymptotically stable. The switching strategy and sub-controllers can also guarantee the closed-loop system is exponentially asymptotically stable even if the switching interval time is constrained.In addition, in response to widespread pulse effect in DPSS, a model of distribution parameters impulsive switched systems (DPISS) was given. The stability of DPISS was also analyzed. Meanwhile, for DPISS, including the nonlinear and uncertain item, their stability was also studied.Finally, the finite-dimensional approximation for distributed parameter systems was studied. The algorithms and approximate rules of GOP were given and convergence was proved on space L~2[a,b]. The optimal approximate control and predictive control for distributed parameter systems have been studied via GOP and the simulation example was given to demonstrate the effectiveness of this method. The switching law is difficult to be obtained for simulation process of DPSS, but the approximate switching law is easy to be obtained via this method and have the simulation process of DPSS finished. An effective way for simulation of DPSS was presented by this method.Besides, simulations are made for main results. Simulation results show the effectiveness of the proposed approaches.更多还原