on Static Feedback for The L1 And Other Optimal Control Problems
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On Static Feedback for the L1 and Other Optimal Control Problems.
Int.\ J.\ Control, 76(5):453--458, 2003
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Abstract
Although l1-optimal linear state feedback controllers are known to be dynamic, it has been shown that suboptimal performance arbitrarily closed to optimal can be achieved by using a static non-linear feedback law. In this paper, this fact is established by using a novel approach which shows that the result is a natural consequence of elementary state-space theory. The approach is motivated by recent works in active vision systems, which have considered a state-feedback problem tightly connected with l1 optimization. This problem, which has independent interest, is discussed in some detail. The new formulation of the problem provides additional insight in l1 state-feedback. In particular, it leads naturally to some extensions which do not follow in a straightforward manner from previous works on the subject.
Co-authors
Bibtex Entry
@article{MirkinRR03a,
title = {On Static Feedback for the L1 and Other Optimal Control Problems},
author = {Leonid Mirkin and Ehud Rivlin and Hector Rotstein},
year = {2003},
journal = {Int.\ J.\ Control},
volume = {76},
number = {5},
pages = {453--458},
abstract = {Although l1-optimal linear state feedback controllers are known to be dynamic, it has been shown that suboptimal performance arbitrarily closed to optimal can be achieved by using a static non-linear feedback law. In this paper, this fact is established by using a novel approach which shows that the result is a natural consequence of elementary state-space theory. The approach is motivated by recent works in active vision systems, which have considered a state-feedback problem tightly connected with l1 optimization. This problem, which has independent interest, is discussed in some detail. The new formulation of the problem provides additional insight in l1 state-feedback. In particular, it leads naturally to some extensions which do not follow in a straightforward manner from previous works on the subject.}
}