基于演算子理论的Hamiltonian系统的鲁棒无源性控制研究

项目名称： 基于演算子理论的Hamiltonian系统的鲁棒无源性控制研究

项目编号： No.61304093

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 步妮

作者单位： 青岛科技大学

项目金额： 25万元

中文摘要： 本项目的研究对象是哈密尔顿系统，作为经典力学三种等价的数学形式体系之一，由于其紧凑的对称结构的优势，在实际中的应用更加广泛，其研究具有重要的理论和实际意义。基于演算子描述的鲁棒右互质分解方法已经被证实是研究非线性系统鲁棒控制的简单有效的方法。因而，本项目中将运用此方法研究哈密尔顿系统的分解和鲁棒无源性控制问题。首先，通过关系映射实现哈密尔顿系统的重新架构，并采用同构思想，实现哈密尔顿系统的分解；其次，选择测试核函数，利用支持向量回归机进行辨识，获得难以建模部分的输出输入关系；再次，设计鲁棒无源性控制器，保证系统的鲁棒稳定性，无源性以及输出能够完全或者渐近跟踪到参考输出；最后，通过铝板热过程的温度控制和能量控制实验来验证所提方法的有效性。本项目问题的解决将把鲁棒右互质分解方法推广到哈密尔顿系统的控制中，是对演算子理论的丰富和发展，对非线性系统的鲁棒和无源性控制具有重要意义。

中文关键词： 鲁棒控制；分解；鲁棒稳定性；辨识；无源性控制

英文摘要： The Hamiltonian system is concerned in this project, as one of the three equivalent mathmatical forms for the classical mechanics, it can be more widely used in the practical application due to its compact symmetric structure, thus the research on Hamiltonian systems plays an important part both in the theoretical and practical applications. The operator based robust right coprime factorization method has been proved to be simple and effective to deal with the robust control of nonlinear systems. Thus, this method will be applied to study the factorization and robust passivity-based control for the Hamiltonian system. Firstly, the Hamiltonian system will be restructured according to the relationship and the factorization of the Hamiltonian system will be realized by means of isomorphism. Then, by selecting and training the kernel functions, the relationship between the output and the input of the unmodelled parts will be obtained by using Support Vector Regression. Further, the robust passivity-based controllers will be designed, in order that the robust stability, passivity and the plant output perfectly or asymptotically track reference output. The effectiveness of the proposed method will be confirmed by the experiments on the temperature control and energy control of the aluminum plate thermal process. This

英文关键词： robust control；factorization/decomposition；robust stability；identification；passivity-based control