Stabilization and Robustness Analysis for a Chain of Saturating Integrators Arising in the Visual Landing of Aircraft

Abstract

We study a chain of saturating integrators with imprecise output measurements. Using a recent backstepping approach that leads to pointwise delays in the control and a dynamic extension, we provide an input-to-state stability result using a bounded control of arbitrarily small amplitude. We apply the result to a problem in the visual landing of aircraft.

Stabilization for a chain of saturating integrators arising in the visual landing of aircraft with sampling

“…In particular, the control design does not significantly simplify in the absence of delays or sampling. Then our conditions in Theorem 1 are similar to those of [13] (and we recover conditions from [1] in the limit asσ → 0), but [13] only asserted a weaker ultimate boundedness result. Another important case is where the δ i 's are zero, in which case we can setδ 1 =δ 2 = 0 in (7) and we can conclude that the closed loop system is uniformly globally asymptotically stable on R 3 .…”

“…Given an appropriate positive constantū, our goal is to design a control u that is valued in [−ū,ū] and that can be computed from the outputs (2) and that renders (1) input-to-state stable with respect to δ = (δ 1 , δ 2 ). Choosingū ∈ (0, L 3 ) allows us to avoid the saturation in (1). Since the state space for (1) is R 3 , this implies as a special case that when δ = 0, all solutions of (1) for all constant initial states x(0) ∈ R 3 will converge to 0 as t → ∞.…”

“…Malisoff was partly supported by NSF Grant 1711299. A special case [1] of this work will appear in the Proceedings of the 58th IEEE Conference on Decision and Control; see Section 1 below for a comparison of this work with [1].…”

“…This paper improves on our preliminary conference version [1], which did not allow sampling or delays in the outputs and did not include complete proofs. Allowing delays or sampling in the outputs is motivated by the image processing in visual landing problems; see our illustration section below.…”