一种用于半无限区间非线性系统最优控制的Laguerre同伦方法
A Laguerre homotopy method for optimal control of nonlinear systems in semi-infinite interval
AI总结：
本文提出一种用于半无限区间最优控制问题的Laguerre同伦方法（LaHOC），特别关注非线性互联大系统。通过谱同伦分析法求解非线性两点边值问题，证明了局部收敛性，并通过数值比较展示其在精度和效率上的优势。
摘要：
本文提出了一种用于半无限区间最优控制问题的Laguerre同伦方法（LaHOC），特别关注非线性互联大系统。在LaHOC中，利用谱同伦分析法推导出非线性两点边值问题的迭代求解器。提供了LaHOC的局部收敛性证明。对两个非线性最优控制问题，将LaHOC、Matlab BVP5C生成的结果与文献结果进行了数值比较。结果表明，LaHOC在精度和效率上均优于其他方法。
英文摘要：
This paper presents a Laguerre homotopy method for optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagins maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.
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