By Gang Tao

ISBN-10: 0471274526

ISBN-13: 9780471274520

Perceiving a necessity for a scientific and unified realizing of adaptive keep watch over concept, electric engineer Tao provides and analyzes universal layout ways with the purpose of masking the basics and state-of-the-art of the sector. Chapters hide structures thought, adaptive parameter estimation, adaptive nation suggestions keep watch over, continuous-time version reference adaptive keep watch over, discrete-time version reference adaptive regulate, oblique adaptive keep watch over, multivariable adaptive keep watch over, and adaptive keep an eye on of structures with nonlinearities.

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**Extra info for Adaptive Control Design and Analysis**

**Sample text**

I| for every (x, p) ∈ K and I ∈ Zn≥0 . 10] to partial derivatives. The point is that the bound for the partial derivatives is uniform in the parameter p. With this in mind, we note that the following are easily checked: 1. the estimate of Sublemma 1 can be extended to the case where f depends in a jointly real analytic manner on a parameter, and the estimate is uniform in the parameter over compact sets; 2. the estimate of Sublemma 2 can be extended to the case where Φ depends in a jointly real analytic manner on a parameter, and the estimate is uniform in the parameter over compact sets; 3.

6. For f ∈ C∞ (M), let us define L f : Γ ∞ (TM) → C∞ (M) X → L X f. 2 by taking U = Γ ∞ (TM), V = C∞ (M), and A = {L f | f ∈ C∞ (M)}. To this end, we make the following definition. 4 (Weak-L Topology for Space of Smooth Vector Fields). For a smooth manifold M, the weak-L topology for Γ ∞ (TM) is the weakest topology for which L f is continuous for every f ∈ C∞ (M), if C∞ (M) has the CO∞ -topology. ◦ We now have the following result. 5 (Weak-L characterisation of CO∞ -Topology for Smooth Vector Fields).

If we have a smooth vector bundle π : E → M, we let (V, ψ) be a vector bundle chart for E inducing a chart (U, φ) for M. For ξ ∈ Γ ∞ (E), the local representative of ξ has the form Rn ⊇ φ(U) x → (x, ξ(x)) ∈ φ(U) × Rk . Thus we have an associated map ξ : φ(U) → Rk that describes the section locally. A CO∞ -subbasic neighbourhood is a subset B∞ (ξ, V, K, , m) of Γ ∞ (E), where 1. ξ ∈ Γ ∞ (E), 2. (V, ψ) is a vector bundle chart for E with associated chart (U, φ) for M, 3. K ⊆ U is compact, 4. ∈ R>0 , 5.

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