周文雅

个人信息Personal Information

副教授

博士生导师

硕士生导师

任职 : 航空航天学院副院长

性别:男

毕业院校:哈尔滨工业大学

学位:博士

所在单位:力学与航空航天学院

学科:飞行器设计. 导航、制导与控制. 动力学与控制

办公地点:大连理工大学海宇楼409B

联系方式:手机:15940819896 电话:0411-84706521 邮箱:zwy@dlut.edu.cn QQ:425039466

电子邮箱:zwy@dlut.edu.cn

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A novel extended precise integration method based on Fourier series expansion for periodic Riccati differential equations

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论文类型:期刊论文

发表时间:2017-11-01

发表刊物:OPTIMAL CONTROL APPLICATIONS & METHODS

收录刊物:SCIE、EI、Scopus

卷号:38

期号:6

页面范围:896-907

ISSN号:0143-2087

关键字:doubling algorithm; Fourier series expansion; periodic Riccati differential equation; periodic system; precise integration method

摘要:A new, reliable algorithm for nonnegative, stabilizing solutions for the periodic Riccati differential equation (PRDE) is proposed based on Fourier series expansion and the precise integration method (PIM). Taking full advantages of periodicity, we expand coefficient matrices of the underlying linear time-varying periodic Hamiltonian system associated with the PRDE in Fourier series, and a novel extended PIM for the transition matrix of linear time-varying periodic systems is developed by combining the doubling algorithm with the increment-storage technique. This method needs to compute the matrix exponential and its related integrals only once for all evenly divided subintervals, which greatly improves the computational efficiency. Further, by introducing the Riccati transformation, a fast recursive formula for the PRDE is derived based on the block form of the transition matrix computed by the extended PIM. Finally, two numerical examples are presented to verify the numerical accuracy and efficiency of the proposed algorithm with compared results.