Range identification for nonlinear parameterizable paracatadioptric systems

Abstract

In this paper, a new range identification technique for a calibrated paracatadioptric system mounted on a moving platform is developed to recover the range information and the three-dimensional (3D) Euclidean coordinates of a static object feature. The position of the moving platform is assumed to be measurable. To identify the unknown range, first, a function of the projected pixel coordinates is related to the unknown 3D Euclidean coordinates of an object feature. This function is nonlinearly parameterized (i.e., the unknown parameters appear nonlinearly in the parameterized model). An adaptive estimator based on a minmax algorithm is then designed to estimate the unknown 3D Euclidean coordinates of an object feature relative to a fixed reference frame which facilitates the identification of range. A Lyapunov-type stability analysis is used to show that the developed estimator provides an estimation of the unknown parameters within a desired precision. Numerical simulation results are presented to illustrate the effectiveness of the proposed range estimation technique. © 2010 Elsevier Ltd. All rights reserved

Online time delay identification and control for general classes of nonlinear systems

“…In [24], it was proven that x ε (t) ∈ L 2 ∩ L ∞ andẋ ε (t) ∈ L ∞ ; thus, from Barbalat's Lemma [25], |x ε (t)| → 0 as t → ∞. From its definition in (5), it is easy to see that |x m (t)| is ultimately bounded in the sense that |x m (t)| ≤ ε as t → ∞.…”

“…Proof: The proof of this theorem is lengthy, and due to space constraints is not presented in this paper, and instead the reader is referred to [24]. In [24], it was proven that x ε (t) ∈ L 2 ∩ L ∞ andẋ ε (t) ∈ L ∞ ; thus, from Barbalat's Lemma [25], |x ε (t)| → 0 as t → ∞.…”

“…Proof: The proof of this theorem is lengthy, and the reader is referred to [26] for the proof or to [24] for a similar proof. It should be noted that, unlike our work, there is no gain matrix in the adaptive update rule in [24].…”

A novel online adaptive time delay identification technique

“…Remark 1: Affine functions always satisfy convexity and concavity defined in Definition 1 [23]. Therefore all affine functions are both convex and concave.…”

“…Proof: Although the systems considered in this work are completely different from the one in [23], and the update law in (18) is slightly different than the one in [23] (i.e. unlike our work, there is no gain matrix in the adaptive update rule (see equation (31)) in [23]), the proof of the theorem is similar to the one in [23]. In this paper, the stability analysis is given in appendix and the reader is referred to [23] for the rest of the proof.…”