System Theory

Download Disturbance Attenuation for Uncertain Control Systems: With by Hans Wilhelm Knobloch PDF

By Hans Wilhelm Knobloch

This booklet offers a survey on fresh makes an attempt to regard classical regulator layout difficulties in case of an doubtful dynamics. it's proven that resource of the uncertainty might be twofold:

(i) The method is below the effect of an exogenous disturbance approximately which one has basically incomplete - or none - information.

(ii) A part of the dynamical legislations is unspecified - because of imperfect modeling.

Both circumstances are defined by means of the kingdom area version in a unified way

“Disturbance Attenuation for doubtful keep watch over platforms” provides a number of ways to the layout challenge within the presence of a (partly) unknown disturbance sign. there's a transparent philosophy underlying each one method which might be characterised by way of both of the subsequent phrases: Adaptive regulate, Worst Case layout, Dissipation Inequalities.

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Read or Download Disturbance Attenuation for Uncertain Control Systems: With Contributions by Alberto Isidori and Dietrich Flockerzi PDF

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Extra resources for Disturbance Attenuation for Uncertain Control Systems: With Contributions by Alberto Isidori and Dietrich Flockerzi

Example text

82) (for pointwise inequalities) or in the sense of the corresponding integrated versions. Case (III). α = 0 and V ≡ V0 is a solution of H0 (t, x, V ) := Vt + H0 (t, x, Vx T ) ≤ 0 . 80) holds for V = V0 , in particular for |v − v ∗ |2S ≥ |v ∗ |2S − 2(v ∗ , β)S = (v ∗ , v ∗ − 2β)S . 5 Alternatives for Affine–Quadratic Systems 33 Note that v ∗ = vH (t, x, (V0 )T x ) is not the worst case strategy of the differential game which is given by vH (t, x, VxT ) with V being a solution of H = 0 (and not of H0 ≤ 0).

Under the above uniformity assumptions one has a step–by–step procedure to follow the actual trajectory by updating V 0 near (t0 , x0 ) to V 1 near (t1 , ξ(t1 )) as above. 68), so that it is sufficient to compute the corresponding local integral manifolds. The above proof also contains an outline for the proof of the following Corollary. 2. Let S be a bounded subset of the (t, x)–space with the following properties. Suppose one can find a δ–neighborhood Sδ of S and numbers m and β such that the following statements hold true: (a) The derivatives of H up to order 2 are bounded in the absolute value by μ on Sδ .

G. disturbance) t → v(t). It is our goal to find mappings (t, x) → u(t, x) and (t, x) → V (t, x) such that a dissipation inequality te t0 f0 (t, x(t), u(t, x(t)), v(t))dt ≤ V (t0 , x0 ) − V (te , x(te )). holds for all disturbances v(·). 72) should exist over [t0 , te ]. It would be advantageous if one could enforce V (te , x(te )) ≥ 0 or if one could prescribe V (te , x(te )) = a(te , x(te )). In the latter case one would have incorporated a terminal pay–off in the costs ˜ 0 , v(·)) = a(te , x(te )) + C(x te t0 f0 (t, x(t), u(t, x(t)), v(t))dt .

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