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With this brief, the authors present algorithms for model-free
stabilization of unstable dynamic systems. An extremum-seeking
algorithm assigns the role of a cost function to the dynamic
system's control Lyapunov function (clf) aiming at its
minimization. The minimization of the clf drives the clf to zero
and achieves asymptotic stabilization. This approach does not rely
on, or require knowledge of, the system model. Instead, it employs
periodic perturbation signals, along with the clf. The same effect
is achieved as by using clf-based feedback laws that profit from
modeling knowledge, but in a time-average sense. Rather than use
integrals of the systems vector field, we employ Lie-bracket-based
(i.e., derivative-based) averaging. The brief contains numerous
examples and applications, including examples with unknown control
directions and experiments with charged particle accelerators. It
is intended for theoretical control engineers and mathematicians,
and practitioners working in various industrial areas and in
robotics.
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Michael Buble
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(1)
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Discovery Miles 4 870
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