最优控制问题的Legendre伪谱法求解及其应用 | |
徐少兵 ; 李升波 ; 成波 ; XU Shao-bing ; LI Sheng-bo ; CHENG Bo | |
2016-03-30 ; 2016-03-30 | |
关键词 | 最优控制 伪谱法 非线性规划 数值求解 concrete fly ash compressive strength model O232 |
其他题名 | Theory and application of Legendre pseudo-spectral method for solving optimal control problem |
中文摘要 | 伪谱法通过全局插值多项式参数化状态和控制变量,将最优控制问题(OCP)转化为非线性规划问题(NLP)进行求解,是一类具有更高求解效率的直接法.总结Legendre伪谱法转化Bolza型最优控制问题的基本框架,推导OCP伴随变量与NLP问题KKT乘子的映射关系,建立基于拟牛顿法的LGL配点数值计算方法,并针对非光滑系统,进一步研究分段伪谱逼近策略.基于上述理论开发通用OCP求解器,并对3个典型最优控制问题进行求解,结果表明了所提出方法和求解器的有效性.; The pseudo-spectral method approximates control and state variables through global interpolation polynomials,then discrete the optimal control problem(OCP) to a nonlinear programming problem(NLP) effectively. It's a kind of direct method with higher solving efficiency. The basic framework of the Legendre pseudo-spectral method converting the Bolza OCP into NLP is summarized, and the mapping between the costates of OCP and the KKT multiplier to NLP is derived.Furthermore, a numerical method is elaborated based on the quasi-Newton method in order to calculate the LGL collocation accurately. The multiphase strategy is also being introduced for non-smooth systems. Finally, a universal optimal control solver POPS(pseudo-spectral optimal control problem solver) is developed based on the Legendre pseudo-spectral method in Matlab. Three typical optimal control problems are solved by using the solver POPS, and the results show the effectiveness of the proposed method and solver POPS. |
语种 | 中文 ; 中文 |
内容类型 | 期刊论文 |
源URL | [http://ir.lib.tsinghua.edu.cn/ir/item.do?handle=123456789/144816] |
专题 | 清华大学 |
推荐引用方式 GB/T 7714 | 徐少兵,李升波,成波,等. 最优控制问题的Legendre伪谱法求解及其应用[J],2016, 2016. |
APA | 徐少兵,李升波,成波,XU Shao-bing,LI Sheng-bo,&CHENG Bo.(2016).最优控制问题的Legendre伪谱法求解及其应用.. |
MLA | 徐少兵,et al."最优控制问题的Legendre伪谱法求解及其应用".(2016). |
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