转移概率部分未知的Markovian跳跃系统的H_∞控制设计

【作者】 杨东；

【导师】 宗广灯；

【作者基本信息】 曲阜师范大学 ， 运筹学与控制论， 2013， 硕士

【摘要】 Markovian跳跃系统是一类特殊而又重要的切换系统,是目前切换系统理论研究的一个前沿方向.与传统的切换系统相比, Markovian跳跃系统具有更复杂的结构,可以更好地描述诸多物理现象,所以现实中的许多过程都可以用Markovian跳跃系统来描述.鉴于不确定性、控制器表现出的脆弱性等因素是导致系统性能变差甚至不稳定的主要原因,最近Markovian跳跃系统的鲁棒稳定性和H∞控制问题受到了广泛关注,也出现了一系列富有价值的结果.然而,这些结果大部分都是基于转移概率完全已知的假设下提出的.在工程实际中, Markovian跳跃系统的转移概率通常是部分未知的.该论文主要针对Markovian跳跃系统在转移概率部分未知的情况下的鲁棒H∞控制问题做了一些理论性的研究.其主要结论包括以下两个部分:1)转移概率部分未知的Markovian跳跃系统的鲁棒有限时间H∞控制.研究了一类Markovian跳跃系统在转移概率部分未知的条件下的鲁棒有限时间H∞控制问题,所考虑的不确定性是范数有界的.首先,给出了Markovian跳跃系统有限时间有界性、H∞有限时间有界性的充分条件.然后,设计了鲁棒有限时间H∞状态反馈控制器.为了计算方便,所有的充分条件都是以严格的线性矩阵不等式给出的.最后,实例表明,所获得的与鲁棒有限时间H∞控制问题相关的充分条件是有效的.2)转移概率部分未知的随机Markovian跳跃系统的鲁棒非脆弱H∞控制.研究了在部分未知转移概率下,带有Markovian跳跃性能的随机系统的鲁棒非脆弱H∞控制器的设计问题,给出了能够保证闭环系统随机镇定性的鲁棒非脆弱H∞状态反馈控制器的设计方法,并且对于所有的不确定性满足规定的H∞衰减指标,其中所设计的鲁棒非脆弱H∞状态反馈控制器是以严格的线性矩阵不等式形式提出的.最后,仿真算例验证了结果的正确性和所提方法的保守性.更多还原

【Abstract】 Markovian jump system is a special and important switched system. Nowadays, moreand more people have paid attention to the study of Markovian jump system. Comparedwith conventional switched system, Markovian jump system has a more richer structureand better describes physical systems. Therefore, many practical processes can be modeledas Markovian jump system. Considering the fact that the uncertainty and non-fragility ofcontroller are the sources of instability, recently, the problems of robust stability and H∞control have been more investigated for Markovian jump system, and many interesting crite-ria have been derived. Usually, it is assumed that the information on transition probabilitieswas completely known for Markovian jump system in many practical applications. However,transition probabilities maybe partially known for most of the real systems. In this thesis,we focus upon the problem of robust H∞control for Markovian jump systems with partiallyknown transition probabilities. The main results are as follows:1) Robust fnite-time H∞control for Markovian jump system with partially knowntransition probabilities.The problem of robust fnite-time H∞control for Markovian jump system with par-tially known transition probabilities is investigated, and the considered uncertainties arenorm-bounded. Sufcient conditions ensuring the fnite-time boundedness, H∞fnite-timeboundedness are respectively developed for the frst time. A robust fnite-time H∞statefeedback controller is also designed, which guarantees the H∞fnite-time boundedness ofthe closed-loop system. Seeking computational convenience, the results are cast in the for-mat of linear matrix inequalities. Finally, a numerical example is provided to demonstratethe efectiveness of the main results.2) Robust non-fragile H∞control for a class of stochastic system under partially knowntransition probabilities.This study concerns the problem of robust non-fragile H∞control for a class of stochasticsystem with partially known transition probabilities. Design a robust non-fragile H∞statefeedback controller, which guarantees the stochastic stability of the closed-loop system anda prescribed H∞attenuation level. Finally, a numerical example is provided to show thefeasibility and validity of the developed results.更多还原