Convergence of Interaction Balance Method Based on Fuzzy Model for Large Scale Systems
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摘要: 结合模糊规划与非线性规划的收敛性分析方法,给出了基于模糊模型的关联平衡法的 收敛性分析.首先证明了经去模糊处理后形成的约束集合与子过程原有的约束集合必有交集. 并且此交集是凸集.在此基础上,分析和证明了基于模糊模型的关联平衡法可用于求解基于模 糊模型的稳态大工业过程递阶优化问题.继而通过定义迭代序列的A-内积,证明了基于模糊模 型的关联平衡法是收敛的.同时给出了保证迭代收敛的迭代系数取值范围.Abstract: This paper studies the convergence of Interaction Balance Method (IBM) based on fuzzy model by combining the analysis of convergence of fuzzy programming and nonlinear programming. Firstly, it is proven that the intersection of the defuzzified and the original constraint sets is nonempty and convex. Secondly, the applicable condition of IBM based on fuzzy model is established. Finally, the convergence of IBM based on fuzzy model is proven by using the definition of the A-norm of iterative sequence, and the range of iteration gain is found for which convergence is guaranteed.
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Key words:
- Fuzzy numbers /
- fuzzy programming /
- interaction balance method
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