一类特殊的h2h∞混合控制问题-a special h2h ∞ hybrid control problem.docxVIP

摘要混合 H2/H∞ 控制问题是很难解决的，近几十年来研究人员一直在研究 这个问题。因此，我们想考虑一些特殊的例子，这些例子可能会对完全的 解决混合 H2/H∞ 控制问题提供一些见解。本论文就是关于带阶约束的混合 H2/H∞ 控制问题。对于给定的一个n 阶被控对象，我们的目标是找到一个阶 数不超过 n 的控制器，使得这个控制器能够满足鲁棒性要求同时还能使闭环 系统的暂态响应表现良好。首先，我们把给定的混合 H2/H∞ 控制问题转化为一个凸优化问题。接 着我们用了一个近似的优化问题, 研究表明，这个问题在状态反馈和输出反 馈的情况下都可以被化成有限维的凸优化问题。我们还做了关于该算法的计 算方面的研究。接着，我们还解决了一个关于原始问题的特殊问题。我们给出了噪声信 号 w 对输出 z1 有影响的凸优化算法。在输出反馈的情况下。最后，我们给 出了所设计的控制器的防真情况。关键词混合 H2/H∞ 控制; 阶约束; 有限维; 凸优化; 鲁棒稳定性AcknowledgementsI would like to express my appreciation to all the people who have given me help and encouragement during the time I studied in HIT ShenZhen Graduate school.First and foremost, I would like to say thanks to my supervisor Professor Li Qiu for his guidance, encouragement and patience in my study and research. He have taught me so much in classical control and robust control theory. He gave me inspiration and suggestions in many aspects. I have benefited a lot from his research attitude and special insights in control theory. With his great help and kind consideration, I finished this thesis.I would also like to say thanks to Professor Zexiang Li and Professor Wei Lin for their excellent lectures on robotic manipulation and nonlinear control. Special thanks to Professor Kemin Zhou for his unforgettable course on robust control.It gives me great pleasure to thank Professor Weizhou Su for taking time to read through my thesis and give me so many valuable suggestions.I have got so much help and support, theoretical and technical, from my friends and colleagues in the control group C2 S2 . The friendly atmosphere of the group made my experience memorable. I especially want to thank Miss Guixian Zhao and Mr Lizhi Hou, they share their research experience with me. And also thanks Mr Feng Wang who offers great help in my practical work.I also want to express my thanks to Dr Yuanqing Wu and his girlfriend, we have spent so much happy time in Shenzhen.Personally I would like to show my great respects to my parents for their support and understa