Abstract:

The usual direct optimization approaches can hardly obtain a “good” numerical solution for the dynamic optimization(DO)problem with control switching structure if the chosen control discretization does not properly reflect the switching structure.In this paper,by reformulating the DO problem as a multi-stage optimization problem,a second exploitation strategy is proposed for solving this problem.The potential control structure can be revealed from the first solution generated by the usual optimization approaches.Subsequently,the DO problem is partitioned as several stages,with each stage corresponding to a particular control arc.A control vector parameterization approach is applied to convert the multi-stage DO problem to a static nonlinear programming(NLP)problem.The control profiles and stage lengths act as decision variables.Based on the Pontryagin maximal principle,a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers.Two examples are studied to demonstrate the effectiveness of this strategy.

Key words: 多级问题动态优化控制切换结构FONT-SIZE: 9pt, mso-bidi-font-family: 宋体, mso-ansi-language: EN-US, mso-fareast-language: ZH-CN, mso-bidi-language: AR-SA, mso-ascii-theme-font: minor-latin, mso-fareast-theme-font: minor-fareast, mso-fareast-font-family: 宋体, mso-hansi-font-family: 宋体" lang=EN-US>;FONT-SIZE: 9pt, mso-bidi-font-family: 宋体, mso-ansi-language: EN-US, mso-fareast-language: ZH-CN, mso-bidi-language: AR-SA, m

摘要：

基于多级表述策略，提出了二次求解具有控制切换结构动态优化问题的数值方法。基于常用的优化方法获得初始控制结构。动态优化问题根据控制结构进行分级，每一级对应一个特定的控制弧段，进而将原问题表述为一个多级动态优化问题。基于控制向量参数化(CVP)，多级动态优化问题转化为一个非线性规划(NLP)问题进行求解。控制参数和级长作为优化变量。基于Pontryagin极大值原理，构造多级伴随系统，进而获得NLP求解器所需的梯度信息。仿真实例验证了方法的有效性。

关键词: 多级问题动态优化控制切换结构FONT-SIZE: 9pt, mso-bidi-font-family: 宋体, mso-ansi-language: EN-US, mso-fareast-language: ZH-CN, mso-bidi-language: AR-SA, mso-ascii-theme-font: minor-latin, mso-fareast-theme-font: minor-fareast, mso-fareast-font-family: 宋体, mso-hansi-font-family: 宋体" lang=EN-US>;FONT-SIZE: 9pt, mso-bidi-font-family: 宋体, mso-ansi-language: EN-US, mso-fareast-language: ZH-CN, mso-bidi-language: AR-SA, m