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Journal Articles SIAM Journal on Control and Optimization Year : 2020

Stabilization for a Perturbed Chain of Integrators in Prescribed Time

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Abstract

In this paper, we consider issues relative to prescribed-time stabilization of a chain of integrators of arbitrary length, either pure (i.e., where there is no disturbance) or perturbed. In the first part, we revisit the proportional navigation feedback (PNF) approach, and we show that it can be appropriately recasted within the framework of time-varying homogeneity. As a first consequence, we recover all previously obtained results on PNF with simpler arguments. We then apply sliding mode-inspired feedbacks to achieve prescribed stabilization with uniformly bounded gains. However, all these feedbacks are robust to matched uncertainties only. In the second part, we provide another sliding mode-inspired feedback which not only stabilizes the pure chain of integrators in prescribed time but also exhibits some robustness in the presence of measurement noise and unmatched uncertainties.
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Dates and versions

hal-02964839 , version 1 (13-10-2020)

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Yacine Chitour, Rosane Ushirobira, Hassan Bouhemou. Stabilization for a Perturbed Chain of Integrators in Prescribed Time. SIAM Journal on Control and Optimization, 2020, ⟨10.1137/19M1285937⟩. ⟨hal-02964839⟩
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