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

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

ISBN-10: 1846283132

ISBN-13: 9781846283130

This ebook comprises chosen contributions via academics on the 3rd annual Formation d’Automatique de Paris. It offers a well-integrated synthesis of the most recent considering in nonlinear optimum keep an eye on, observer layout, balance research and structural houses of linear structures, with no the necessity for an exhaustive literature assessment. The the world over recognized participants to this quantity characterize a number of the so much respected regulate facilities in Europe.

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This property is crucial to understand the orbit transfer problem. 4 Time-optimal Transfer Between Keplerian Orbits An important matter in astronautics is to transfer a satellite between elliptic orbits. Optimal criterions related to this issue are the maximization of the final mass (which amounts to minimizing the fuel consumption) or the minimization of the transfer time. We shall consider this second problem for two reasons. First, recent research projects concern orbit transfer with electroionic propulsion for which the thrust is very low and the transfer duration very long (up to several months).

As previously, we make the following regularity assumptions: (i) The strict Legendre-Clebsch conditions holds along the extremal, ∂2H (¯ z (t), u ¯(t)) < 0, t ∈ [0, T ]. ∂u2 (ii) On each subinterval 0 < t0 < t1 ≤ T the singularity is of codimension one. (iii)We are in the normal case where H = p, f (x, u) is not zero and p can be chosen on the level set H = −1 + p, f (x, u) = 0. In this case, our reference control is smooth and the reference extremal is solution of a system defined by a smooth Hamiltonian Hr .

The maximization of the m Hamiltonian H = H0 + i=1 ui Hi outside Σ implies that ui = Hi m i=1 Hi2 , i = 1, . . , m. 22) into H, one defines the Hamiltonian function m Hr = H 0 + 1 2 Hi2 . 13. The corresponding solutions are called order zero extremals. From the maximum principle, optimal extremals are contained in the level set {Hr ≥ 0}. Those in {Hr = 0} are exceptional. The following result is standard. 19. The order zero extremals are smooth responses to smooth controls on the boundary of |u| ≤ 1.

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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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