Abstract
The paper is concerned with the Taylor expansion of trajectories of the system ẋ = Σ f i (x)u i in terms of iterated integrals of the controls. Formulas are derived for the approximation of tangent and cotangent vectors and of their high order time derivatives, together with directional error estimates. These results are relevant for the analysis of local optimization problems, using high order nilpotent approximations.
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© 1991 Birkhäuser Boston
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Bressan, A. (1991). Nilpotent Approximations and Optimal Trajectories. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_9
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
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