Convergence monotonicity and speed comparison of iterative learning control algorithms for nonlinear systems
Release Time:2025-04-30
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- Date:
- 2025-04-30
- Title of Paper:
- Convergence monotonicity and speed comparison of iterative learning control algorithms for nonlinear systems
- Journal:
- IMA Journal of Mathematical Control and Information
- Summary:
- In this paper, conventional first- and second-order proportional-derivative-type (PD-type) iterative learning
control (ILC) updating algorithms are discussed for a type of nonlinear time-invariant system. On the
basis of the Bellman–Gronwall inequality, the convergence is derived in the sense that the tracking error
is measured in the form of the Lebesgue-p norm. This analysis shows that, under an appropriate condition,
the first-order PD-type ILC updating law is monotonically convergent while the second-order law
is convergent and the monotonicity is guaranteed after finite iterations. Further, by analysing the characteristic
polynomial of the second-order PD-type ILC updating law, an argument about the comparison of
convergence speed in terms of Qp-factor is made. The argument clarifies that the second-order PD-type
ILC law can be Qp faster, equivalent or slower than the first-order law, depending upon different sets of
the learning gains. Numerical simulations are conducted to show their validity and effectiveness.
- Co-author:
- Xiaoe Ruan, Jianyong Zhao
- Volume:
- (2013) 30,
- Page Number:
- 473–486
- Translation or Not:
- No
- Date of Publication:
- 2013-07-01