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A simple learning control algorithm is designed which guarantees asymptotic output tracking for any initial condition belonging to any given connected compact set.
uniformly for in any compact set.
Since is continuous, it is uniformly continuous on any compact set.
if for any compact set K ⊂ M ⊂ R n, we have.
Then is bounded and uniformly continuous on for any compact set in.
For any compact set there exists a constant such that for all for all for all and.
Suppose that, for any compact set (mathcal {D}subsetmathcal{Z}), let (d =sup{Vert z-z^{0}Vert _{G}vert zinmathcal {D}}).
and, for any compact set, we denote by the set of all the functions such that (1.7) is replaced by (2.2).
As a result, for any, Since is a weak* compact set, we have (2.28).
Furthermore, any subset of an I-ward compact set is I-ward compact, and any bounded subset of R is I-ward compact.
Furthermore, the intersection of (mathbb{T}) with any closed bounded interval is a compact set.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com