Dual Linera Programming Approach for Parameter Uncertainty Interval Estimation
-
摘要: 将参数不定区间估计(PIE)问题变换成一组对偶线性规划(DLP)问题,提出了求解这组DLP问题的改进单纯形方法.该方法利用变量间的对偶关系,直接计算初始基本可行解,省去了初始基本可行解的搜索步骤.此外,在确定旋入和旋出变量时都采用了目标值最大减少规则,减少了旋转迭代次数.针对由PIE问题所导出的全部DLP问题都具有相同的目标函数和约束矩阵,给出了单搜索过程求解全部DLP问题的联合单纯形法.仿真结果说明了所给算法的计算效率.Abstract: The parameter uncertainty interval estimation (PIE) problem was transferred into a set of dual linear programming (DLP) problems, and an improved simplex method was proposed to solve these DLP problems. The dual relationship between the variables of the DLP problems was used to directly compute an initial basic feasible solution, so that the process of finding an initial basic feasible solution is removed. Moreover, the largest reduction rule was used in the determination of both entering and leaving variables, and thus the iterative number was reduced. Considering that all the DLP problems derived from a PIE problem have the same objective function and constraint matrix, a unified simplex method was given to solve all the DLP problems in a single searching procedure. Simulation results show the effectiveness of the proposed algorithm.
-
[1] Ljung L. System identification:theory for user[M]. Second edition. Prentice Hall, 1999 [2] 孙先仿. 集员辨识:算法、收敛性和鲁棒性. 北京:中国科学院自动化研究所, 1994 Sun Xianfang. Set membership identification:algorithms, convergence and robustness. Beijing:Institute of Automation, Chinese Academy of Sciences, 1994(in Chinese) [3] Milanese M, Belforte G. Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors:linear families of models and estimators[J]. IEEE Trans Autom Control, 1982, 27(2):408~414 [4] Fang S C, Puthenpura S. Linear optimization and extensions:theory and algorithms[M]. Prentice Hall Inc, 1993 [5] Barrodale I, Roberts F D K. An improved algorithm for discrete L1 linear approximation[J]. SIAM J Numer Anal, 1973, 5:839~848 [6] Tzes A, Hu Q, Le K. Development of a recursive algorithm for parameter uncertainty interval estimation. Proceedings of 34th IEEE Conf. Decision and Control. New Orleans:IEEE,1995. 3010~3015 [7] 许万蓉.线性规划[M].北京:北京理工大学出版社,1988 Xu Wanrong. Linear programming[M]. Beijing:Beijing Institute of Technology Press, 1988(in Chinese) [8] 王书宁,黄学俊,戴建设.线性模型参数l∞和l1中心估计量的统一求法[J]. 自动化学报, 1996, 22 (3):353~356 Wang Shuning, Huang Xuejun, Dai Jianshe. Computing l∞ and l1 central estimators of linear models' parameters with a general method[J]. Acta Automatica Sinica, 1996, 22(3):353~356(in Chinese) -
点击查看大图
计量
- 文章访问数: 2024
- HTML全文浏览量: 39
- PDF下载量: 2
- 被引次数: 0
下载:
