By Hans Wilhelm Knobloch
ISBN-10: 3319009567
ISBN-13: 9783319009568
ISBN-10: 3319009575
ISBN-13: 9783319009575
This e-book offers a survey on contemporary makes an attempt to regard classical regulator layout difficulties in case of an doubtful dynamics. it truly is proven that resource of the uncertainty will be twofold:
(i) The process is less than the effect of an exogenous disturbance approximately which one has basically incomplete - or none - information.
(ii) A component of the dynamical legislations is unspecified - because of imperfect modeling.
Both situations are defined via the country area version in a unified way
“Disturbance Attenuation for doubtful regulate platforms” provides various ways to the layout challenge within the presence of a (partly) unknown disturbance sign. there's a transparent philosophy underlying each one strategy which might be characterised via both of the subsequent phrases: Adaptive regulate, Worst Case layout, Dissipation Inequalities.
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Additional info for Disturbance Attenuation for Uncertain Control Systems: With Contributions by Alberto Isidori and Dietrich Flockerzi
Example text
1, we repeat it for the readers convenience. 3. 4 Local Solutions of Hamilton–Jacobi PDEs 25 in the (t, x)–space. 1. Assume that for ˜(t) of the initial value problem each τ ∈ [ τ0 , τe ] the solution x x˙ = f t, x, uH (t, x, S(t, x)), vH (t, x, S(t, x)) , x(τ ) = ζ(τ ) exists and satisfies on some interval [ τ, te ], te ≥ τ , (t, x˜(t)) ∈ S0 , ψ(te , x˜(te )) = 0 . e. 45). The solutions x˜(t) mentioned in the statement of the proposition clearly can be supplemented by y˜(t) = S(t, x ˜(t)) to yield an embeddable characteristic.
55) holds true. 56)) admits the solution = 0. This in turn is true if (0) ˜2 (t), y˜(0) (t)) = 0, Hx2 x2 (t, x t0 ≤ t ≤ t2 . 57) Now we have, if we write ψ = (ψ1 , . . , ψn1 )T and x1 = (x11 , . . 58) ν=1 plus terms which do not depend upon Mν . 57) by a proper choice of the Mν . Before we proceed we wish to state several consequences of the previous relations , cf. 59) (0) (0) ˙ (0) (0) ˙ (0) ˙ ˜1 (t0 ) + y˜x2 (x )x ˜2 (t0 ) (S)t (t0 , x2 ) = y˜0 (t0 ) = y˜x1 (x )x = y˜x1 (x(0) )c0 + y˜x2 (x(0) )(p2 (x(0) ) + B2 (x(0) )u0 ) .
Conclusion. 70) (p1 (x(t)) − p1 (x(0) )) dt t0 holds if δ = te − t0 > 0 is sufficiently small. 3) for some continuous v(t) and u=u ˆ0 (t, x) := u ˇ(x, λ0 , S(t, x2 )) . 71) Proof. 32) is satisfied. To this purpose we make a formal state augmentation. e. we prolong p2 by the component to x2 a variable ξ satisfying the de. ξ=1 1 and B2 by the row vector 0. 32) holds true. The second condition is clearly satisfied since the vector p2 + B2 u0 has the new component 1. e. 1 ✷ runs exactly as before. 3. 46), then the integrand in the above expression is changed to + λT u(x) − u ˆ0 (t, x)) 0 B1 (x)(˜ 1 λT B1 (x)B2 (x)T (˜ q(x) + κ u ˆ0 (t, x) 2 − y (x) − S(t, x2 )), 2κ 0 q(x) + κ u ˆ0 (t, x) = 2 x = x(t).
Disturbance Attenuation for Uncertain Control Systems: With Contributions by Alberto Isidori and Dietrich Flockerzi by Hans Wilhelm Knobloch
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