自适应控制向量参数化动态优化研究

发布时间：2018-03-25 19:10

本文选题：动态优化　切入点：控制向量参数化　出处：《浙江大学》2017年硕士论文

【摘要】：动态优化,是解决实际生产过程瓶颈问题、实现最优控制的有效手段,广泛应用于生产生活的诸多领域,受到国内外众多专家学者的关注与研究。控制向量参数化(CVP)方法是其中的一种主流计算方法,通过对控制变量进行离散,将原动态优化问题转化为一个新的非线性规划(NLP)问题来求解。目前,如何以较低的计算成本获得较高的求解质量是CVP方法中的研究热点之一。本文以自适应CVP方法为框架,针对其两个求解阶段,即控制变量离散化和NLP问题求解,着重于效率的提升,进行了一定研究。本文的主要创新性工作如下:(1)针对如何高效求解动态优化问题这一研究热点,提出了一种具有一般性的自适应CVP动态优化框架。以该框架为基础,采用一定的分析方法,可由粗糙的时间网格自适应地得到经济、合理的时间网格,从而提高求解效率。(2)以基于小波分析的自适应CVP方法为基础,提出了一种重要时间节点优化方法。该方法可以准确探测出重要时间节点的所属区域,并进行针对性优化,从而以较小的代价实现对重要节点的精确逼近,尤其对于含有跳变时间节点的问题十分有效。(3)从改善目标函数值的角度,提出了一种基于灵敏度分析的自适应CVP方法,并进一步将重要时间节点优化方法引入其中。该自适应方法只在能够显著改善目标值的区域插入新节点,减少了时间网格中的不必要节点,大大提高了求解效率。实例测试表明,该方法还具有较高的鲁棒性。(4)针对带约束NLP问题,提出了一种新的非单调过滤线搜索技术,并将其引入Wachter-Biegler内点法框架中,获得良好数值表现。所提出的非单调技术使得步长搜索更加灵活、宽松,对于算法整体性能的提升起到重要作用。
[Abstract]:Dynamic optimization is an effective means to solve the bottleneck problem of actual production process and to realize optimal control. It is widely used in many fields of production and life. The control vector parameterization (CVP) method is one of the mainstream computing methods, which discretize the control variables. The original dynamic optimization problem is transformed into a new nonlinear programming problem to be solved. At present, it is one of the research hotspots in CVP method that how to obtain higher solution quality at lower computational cost. In this paper, adaptive CVP method is used as a framework. In view of the two stages of solving the control variable discretization and the NLP problem, the paper focuses on the improvement of efficiency, and makes a certain research. The main innovative work of this paper is as follows: 1) how to solve the dynamic optimization problem efficiently is a hot research topic. In this paper, a general adaptive CVP dynamic optimization framework is proposed. Based on this framework and using a certain analysis method, the economic and reasonable time grids can be obtained adaptively from rough time grids. Based on the adaptive CVP method based on wavelet analysis, an important time node optimization method is proposed, which can accurately detect the region of the important time node and optimize it pertinently. In order to achieve accurate approximation of important nodes at a lower cost, especially for the problem with jump time nodes, an adaptive CVP method based on sensitivity analysis is proposed to improve the value of objective function. Furthermore, the important time node optimization method is introduced. The adaptive method only inserts new nodes in the area where the target value can be significantly improved, thus reducing the unnecessary nodes in the time grid. The test results show that the proposed method is robust to the constrained NLP problem, and a new non-monotone filtering line search technique is proposed, which is introduced into the framework of the Wachter-Biegler interior point method. The proposed non-monotone technique makes the step size search more flexible and relaxed, and plays an important role in improving the overall performance of the algorithm.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221.2

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