随机系统的时滞镇定和鲁棒控制

【作者】 张彦良；

【导师】 王志明；

【作者基本信息】 武汉科技大学 ， 概率论与数理统计， 2011， 硕士

【摘要】 随机控制理论广泛地应用于经济、人口系统等社会领域以及航空航天、导航与控制、制造工程等工程领域。随机系统的研究已成为现代控制理论研究中的一个热点问题。在实际系统中,非线性、时滞是普遍存在的,通常时滞是引起系统不稳定或产生振荡的根源。另一方面,被控系统往往受到一些参数误差、未建模动态以及不确定的外界干扰等不确定因素的影响,系统模型具有某种不确定性。控制界针对不确定性对系统性能影响的研究产生了鲁棒控制理论。因此,随机系统的时滞镇定和鲁棒控制研究就具有重要的理论研究意义和实际应用价值。本文首先构造一个Lyapunov‐Krasovskii泛函,利用Ito微分公式结合线性矩阵不等式(LMI)技术,研究了一类随机系统的时滞反馈鲁棒镇定和鲁棒H_∞控制问题,给出了系统随机稳定和满足随机H_∞性能指标的充分条件,得到了随机系统时滞反馈镇定和鲁棒H_∞控制器的设计方法,并通过仿真算例说明了方法的有效性。进而,对该类系统考虑了当系统状态不能直接得到时,利用Ito微分结合非线性矩阵不等式(NMI)和半线性矩阵不等式研究了随机动态输出时滞反馈镇定和H_∞控制问题并给出了随机动态输出时滞反馈控制器的设计方法。这类控制器不同于传统的状态反馈控制器和状态输出反馈控制器。并且通过数值仿真说明了方法的有效性和结论的正确性。最后对全文进行了总结,并对未来的研究方向进行了展望。更多还原

【Abstract】 Stochastic control theory is widely used in economy, population system, social fields and aerospace, navigation and control, manufacturing engineering and engineering field. Stochastic system research has become one of a hot issue of modern control theory research. In the actual system, nonlinear, delay is universal exist, delay usually causing the instability or produce the root of oscillation. On the other hand, control system often affected by uncertainty factors like Parameter errors,Unmodeled dynamics and uncertainty outside interference. System model has some kind of uncertainty .Field of control produces robust control theory bases on the uncertainties on system performance impact study. Therefore, the delay stabilization and robust control problems for stochastic systems have important theoretical research significance and actual application value.In this paper, we construct a Lyapunov-Krasovskii functional firstly, the delay feedback robust stabilization and H_∞control problems for a class of stochastic system are reserched by Ito? differential formula and linear matrix inequality(LMI) techniques, the delay-dependent sufficient conditions which provide the feasibility of the H_∞controller are given. The numerical example with simulation also has given to show the feasibility and effectiveness of the proposed method.Secondly,the states of the stochastic systems under consideration in chapter 4 are not available directly, the stochastic dynamic output feedback stabilization and delay control problems are studied by Ito? differential formula, linear matrix inequality(LMI) and bilinear matrix inequality (BMI)techniques, and given the design method of stochastic dynamic output feedback controller. This kind of controller is different from traditional state feedback controller and state output feedback controller. The feasibility and effectiveness of the proposed method and the correctness of the conclusion are shown by the illustrate numerical example .At last,we summarize the full text and gives the future research direction.更多还原