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

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

This publication comprises chosen contributions by way of academics on the 3rd annual Formation d’Automatique de Paris. It presents a well-integrated synthesis of the newest pondering in nonlinear optimum keep watch over, observer layout, balance research and structural homes of linear platforms, with no the necessity for an exhaustive literature evaluation. The the world over recognized members to this quantity characterize a number of the such a lot respected keep watch over facilities in Europe.

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The aim of this section is twofold. First, thanks to the concept of conjugate point, we obtain second-order necessary and sufficient conditions for optimality, the set of controls being endowed with the L∞ topology. Then, using standard field theory, we extend those optimality results to the C 0 topology on the set of trajectories of the system. In order to carry out a more complete analysis applicable to affine systems, we make the following prolongation. We set u˙ = v and extend the original system to a control affine one: x˙ = f (x, u) u˙ = v.

0) in suitable coordinates x = (x1 , . . , xn ). A tubular neighbourhood of γ is characterized by small xi ’s for i ≥ 2. Then we consider the Taylor expansion of the pair F0 , F1 along γ: the jet of order one (resp. two) is the collection of all linear (resp. quadratic) terms. 1). Besides, if F1 is tranverse to γ, we can choose the coordinates in the neighbourhood of the curve such that F1 is identified with ∂/∂xn . From our preliminary analysis, we know that the first order Fr´echet derivative of the endpoint mapping depends only upon the jet of order one, while the secondorder intrinsic derivative depends only upon the jet of order two.

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). Moreover, since the transfer is always with maximum thrust, the structure of the minimum time extremals is simpler than in the minimum consumption case [10] and fit in the smooth case previously analyzed. 1 Model and Basic Properties Let m be the mass of the satellite, and let F be the thrust of the engine.

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