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Convergence Properties of Iterative Learning Control Processes in the Sense of the Lebesgue‐ P Norm
Author(s) -
Ruan Xiaoe,
Bien Z. Zenn,
Wang Qi
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.425
Subject(s) - iterative learning control , monotonic function , monotone polygon , mathematics , norm (philosophy) , convergence (economics) , lebesgue integration , dominated convergence theorem , convergence tests , normal convergence , discrete mathematics , computer science , rate of convergence , control (management) , mathematical analysis , channel (broadcasting) , artificial intelligence , computer network , geometry , political science , law , economics , economic growth
This paper addresses the convergence issue of first‐order and second‐order PD‐type iterative learning control schemes for a type of partially known linear time‐invariant systems. By taking advantage of the generalized Young inequality of convolution integral, the convergence is analyzed in the sense of the Lebesgue‐ p norm and the convergence speed is also discussed in terms of Q p factors. Specifically, we find that: (1) the sufficient condition on convergence is dominated not only by the derivative learning gains, along with the system input and output matrices, but also by the proportional learning gains and the system state matrix; (2) the strictly monotone convergence is guaranteed for the first‐order rule while, in the case of the second‐order scheme, the monotonicity is maintained after some finite number of iterations; and (3) the iterative learning process performed by the second‐order learning scheme can be Q p ‐faster, Q p ‐equivalent, or Q p ‐slower than the iterative learning process manipulated by the first‐order rule if the learning gains are appropriately chosen. To manifest the validity and effectiveness of the results, several numerical simulations are conducted. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society