Download PDF by Julio Antonio Loría Perez, Françoise Lamnabhi-Lagarrigue,: Advanced Topics in Control Systems Theory: Lecture Notes

By Julio Antonio Loría Perez, Françoise Lamnabhi-Lagarrigue, Elena Viatcheslavovna Panteley

ISBN-10: 1846283132

ISBN-13: 9781846283130

This ebook contains chosen contributions by means of academics on the 3rd annual Formation d’Automatique de Paris. It presents a well-integrated synthesis of the newest considering in nonlinear optimum regulate, observer layout, balance research and structural homes of linear structures, with out the necessity for an exhaustive literature evaluation. The the world over identified participants to this quantity signify the various so much respected regulate facilities in Europe.

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Additional info for Advanced Topics in Control Systems Theory: Lecture Notes from FAP 2005

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Decomposing S into n × n blocks, S= AB CD we obtain the relations: t AD = tBC = I, tAC = tCA, tBD = tDB. The Lie algebra sp(n, R) of Sp(n, R) is the algebra of order 2n matrices H such that exp tH is in Sp(n, R). These matrices are characterized by tHJ +H tJ = 0 and, decomposing H into blocks, H= AB CD we obtain the equivalent definition: sp(n, R) = {H = A B , B and C symmetric} · · · C − tA 22 Bernard Bonnard and Jean-Baptiste Caillau The symplectic group acts on Lagrangian subspaces and we have the following representation of Lagrangian subspaces.

If q ∧ q˙ is not zero, the thrust can be decomposed in a moving frame attached to the satellite. A canonical choice consists in the radial-orthoradial frame: F = ur Fr + uor For + uc Fc with Fr = q ∧ q˙ ∂ q ∂ , Fc = r ∂ q˙ |q ∧ q| ˙ ∂ q˙ and For = Fc ∧ Fr . If uc = 0, the state space is the tangent space to the osculating plane generated by q and q˙ and we have a 2D-problem. For the sake of simplicity, we shall restrict our study to this setting which already exhibits all the relevant features of the whole system.

Then, differentiating as before H1 (z) = 0, one gets that, everywhere p(t), adk F0 · F1 (γ(t)) = 0, k ≥ 0. We proved the following. 4. Let z be a smooth singular extremal on [0, T ], corresponding to a singular control identified to zero. 12) everywhere on [0, T ]. 12), adk H0 · H1 denotes the k-th Poisson bracket of H1 with H0 . This is clearly equivalent to the following lemma. 3. Let x be a trajectory defined on [0, T ] and associated to the zero control. Assume that, for each t, V1 (t) = Span{adk F0 · F1 (x(t)), k ≥ 0} is of maximum rank n.

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Advanced Topics in Control Systems Theory: Lecture Notes from FAP 2005 by Julio Antonio Loría Perez, Françoise Lamnabhi-Lagarrigue, Elena Viatcheslavovna Panteley

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