ABSTRACT

This study is aimed to relate nonlinear infinite-horizon optimal control problems (NLIHOCPs) with open-loop information. The difficulties of solving the two-point boundary value problems (TPBVPs) arising from NLIHOCPs can be assigned to the nonlinearity of differential equations, the combination of split boundary conditions, and how the transversality conditions in infinite-horizon are treated. In this paper, we propose a combined quasilinearization method (QLM) with the exponential Bernstein functions (EBFs) for solving nonlinear TPBVPs on the semi-infinite domain. First, the QLM is used to reduce the nonlinear TPBVP to a sequence of linear differential equations. Then, a collocation method based on the EBFs is utilized to find the approximate solution of the resulting linear differential equations. By applying the EBFs, the transversality conditions for TPBVP on the semi-infinite domain are satisfied. The convergence of the QLM + EBFs is proved. Some numerical experiments are performed to confirm the validity of the proposed computational scheme.

摘要

本研究旨在将非线性无限水平最优控制问题 (NLIHOCP) 与开环信息联系起来。求解 NLIHOCP 引起的两点边值问题 (TPBVP) 的困难可以归结为微分方程的非线性、分裂边界条件的组合以及如何处理无限视域中的横向条件。在本文中，我们提出了一种组合拟线性化方法 (QLM) 与指数 Bernstein 函数 (EBF)，用于解决半无限域上的非线性 TPBVP。首先，QLM 用于将非线性 TPBVP 简化为线性微分方程序列。然后，利用基于 EBF 的搭配方法来寻找所得线性微分方程的近似解。通过应用 EBF，满足 TPBVP 在半无限域上的横向条件。证明了 QLM + EBF 的收敛性。进行了一些数值实验以确认所提出的计算方案的有效性。