Iterative Chebyshev approximation method for optimal control problems

报告人：Kok Lay Teo教授（澳大利亚科廷大学）

时 间：2024年4月8日 16:30-17:30

地 点：博学楼506会议室

主办单位：贵州大学数学与统计学院

Abstract

This talk presents a novel numerical approach for solving nonlinear constrained optimal control problems (NCOCPs). Instead of directly solving the NCOCPs, the dynamic system and constraints are linearized, resulting in a sequence of sub problems. For each sub-problem, the Chebyshev series approximates the state and control functions. To eliminate the non-collocation point errors caused by conventional collocation methods, the Chebyshev series is used to approximate the coefficient functions of the linear dynamic system and constraints. By leveraging the properties of Chebyshev polynomials, the approximate sub-problem can be transformed into an equivalent nonlinear optimization problem with linear equality constraints. Therefore, any feasible solution to the approximate sub-problem will satisfy its dynamic system and constraints over the entire time horizon. Three examples are solved to validate the proposed method's efficacy. The numerical results obtained show that the proposed approach is highly accurate compared to the Chebyshev pseudo-spectral method.

个人简介

马来西亚双威大学数学科学学院教授、副院长，澳大利亚科廷大学（Curtin University）荣誉退休教授，国际系统与控制论科学院（IASCYS）院士、亚太人工智能协会（AAIA）会士、澳大利亚数学学会（AustMS）会士和IEEE终身高级会员。博士毕业于加拿大渥太华大学，1998年至2005年任香港理工大学应用数学系的首席教授和系主任，2005年至2010年任澳大利亚科廷大学数学与统计系的首席教授和系主任，2011年至2019年任科廷大学John Curtin杰出贡献教授（John Curtin Distinguished Professor）。张教授主要从事最优控制、优化理论与应用、通讯信号处理、金融优化决策理论等方面研究。