广义系统的次优控制

【作者】 侯冬梅；

【导师】 张显；

【作者基本信息】 黑龙江大学 ， 应用数学， 2008， 硕士

【摘要】 广义系统自20世纪70年代产生以来,由于在宇航系统、电力系统、机器人系统、生物系统、化工系统、经济系统及电路系统等领域的广泛应用,引起了广大学者的极大兴趣,其理论研究取得了很大的进展,许多正常系统的结论相继被推广到广义系统。在二次最优控制方面涌现出不少的优秀成果,但是广义系统的次优控制问题的讨论成果很少,由于在实际工程中,对于工程设计问题,不一定要求找到严格实现“最优问题”的控制器,只要能找到满足工程设计要求的控制器即可,于是研究次优控制问题具有很大的必要性。近年来,非方广义系统被广泛研究,但次优控制的成果很少。本文详细的分析了非方广义系统以及广义系统的次优控制问题的研究状况,并通过使用半受限等价变换和广义逆矩阵将陈莉在文献[山东大学学报,2006,41(2):74-77]中研究的非方广义系统系统带干扰抑制的LQ次优控制问题中的参数限制条件替换为更容易寻找的系数矩阵的秩约束条件,仍可得到次优控制-状态对存在,并且闭环系统性能指标被控制在尽量小的范围内,次优控制可被综合为状态反馈,闭环系统任意有限特征值均落在开左半复平面.此方法使问题的求解更容易,所以利于工程实现。更多还原

【Abstract】 Since 1970s singular systems were raised, as it was used widely in aerospace system, power system, robot system, biological system, chemical system, ecnomic system and circuit system, and so on, so it provoked interest of many scholars. The study of its theory has been made a great progress. Some conclusions of linear system have been extended to singular systems. There have been many excellent results related to linear quadratic optimal control problem, but few in suboptimal control problem of singular systems. For the design of pratical projects, we do not need find accurate optimal regulator, we only need to find the regulator which satisfied the desigin requirement, so it is necessary to reserach suboptimal control problem. In recent years, nonregular singular systems were widely discussed, but few results about suboptimal control problem.In this thesis, we analyse the exisiting results of nonregular singular systems and suboptimal control problem of singular systems. Using semirestrictied equivalent transformations and Moore-Penrose generalized inverses of matrices, we replace the restricted condition of parameters in [Journal of Shandong University,2006,41(2):74-77] by some rank conditions of coefficient matrices. A suboptiaml control-state pair is constructed, which ensures the performance of the close-loop system is within certain range. The suboptiaml control can be synthesized as state feedback, and all the finite eigenvalues of the close-loop are located on the open left-half complex plane. The method is easier to caculate the solution, so it is convenient to applications in enginearing.更多还原