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一类输入时滞的不确定多时滞非线性系统的新型自适应$H^{\infty}$控制

柴琳,费树岷   

  1. 东南大学自动控制系自动化研究所, 南京 210096
  • 收稿日期:2005-04-21 修回日期:2005-12-01 出版日期:2007-12-25 发布日期:2007-12-25

柴琳;费树岷 . 一类输入时滞的不确定多时滞非线性系统的新型自适应$H^{\infty}$控制[J]. 系统科学与数学, 2007, 27(6): 880-891.

Chai Lin;Fei Shumin. A New Approach of Adaptive $H^{\Infty}$ Control for a Class ofUncertain Nonlinear Time--Delay System with Multiple Time Delayand Uncertain Input Delay[J]. Journal of Systems Science and Mathematical Sciences, 2007, 27(6): 880-891.

A New Approach of Adaptive $H^{\Infty}$ Control for a Class ofUncertain Nonlinear Time--Delay System with Multiple Time Delayand Uncertain Input Delay

Chai Lin, Fei Shumin   

  1. Department of Automation, Southeast University, Nanjing 210096
  • Received:2005-04-21 Revised:2005-12-01 Online:2007-12-25 Published:2007-12-25
针对一类带未知输入时滞参数且含未知上界的不确定非线性环节的时滞系统,基于LMI方法,采用一种基于``descriptor form"的Lyapunov-Krasovskii泛函方法和新型的带记忆的状态反馈控制,使得时滞参数、未知上界向量这两种参数的自适应律均能反映其实时估计值与其实际接近值之间的差值,从而突破以往自适应控制对估计值的大小限制和保证限制成立的``调整参数"计算的困难,给出了针对这两种参数的新型自适应$H^{\infty}$控制器的设计方案,一仿真实例证明了该控制方案的有效性.
A method of LMI, a kind of Lyapunov-Krasovskii functional, which is based on ``descriptor form", and a new type of memory state feedback controller are used to solve the problem of $H^{\infty}$ controller, designing new adaptive strategies for two unknown constant: input delay and up bound for norm of the uncertain nonlinear part. This type of strategy isn't limited in the estimate value as that of the old adaptive controllers and manages to avoid calculating ``adjusting constant", which guarantees the limitation as the old adaptive
controllers, by reflecting difference between the estimate value and the value being close to the practical. The sufficient condition of its solution is given with a numerical example.

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