论文标题
使用傅立叶积分伪谱法的非线性周期性最佳控制问题的数值解决方案
Numerical Solution of Nonlinear Periodic Optimal Control Problems Using a Fourier Integral Pseudospectral Method
论文作者
论文摘要
本文介绍了一类非线性，周期性最佳控制（OC）问题的傅立叶积分伪谱（FIPS）方法，具有平等性和/或不平等约束以及足够平滑的解决方案。在此方案中，该问题的积分形式在一个稳定的节点集中置于相处，并使用高度准确的傅立叶集成矩阵（FIMS）近似所有必要的积分。提出的方法导致具有代数约束的非线性编程问题（NLP），该方法使用直接的数值优化方法求解。对于傅立叶系列，插值和用于平滑和连续的周期性功能的四次序列，得出了尖锐的收敛性和误差估计。两个非线性示例被认为显示了数值方案的准确性和效率。
This paper presents a Fourier integral pseudospectral (FIPS) method for a general class of nonlinear, periodic optimal control (OC) problems with equality and/or inequality constraints and sufficiently smooth solutions. In this scheme, the integral form of the problem is collocated at an equispaced set of nodes, and all necessary integrals are approximated using highly accurate Fourier integration matrices (FIMs). The proposed method leads to a nonlinear programming problem (NLP) with algebraic constraints, which is solved using a direct numerical optimization method. Sharp convergence and error estimates are derived for Fourier series, interpolants, and quadratures used for smooth and continuous periodic functions. Two nonlinear examples are considered to show the accuracy and efficiency of the numerical scheme.
