SO(3)-invariant asymptotic observers for dense depth field estimation based on visual data and known camera motion

In this paper, we use known camera motion associated to a video sequence of a static scene in order to estimate and incrementally refine the surrounding depth field. We exploit the SO(3)-invariance of brightness and depth fields dynamics to customize standard image processing techniques. Inspired by the Horn-Schunck method, we propose a SO(3)-invariant cost to estimate the depth field. At each time step, this provides a diffusion equation on the unit Riemannian sphere that is numerically solved to obtain a real time depth field estimation of the entire field of view. Two asymptotic observers are derived from the governing equations of dynamics, respectively based on optical flow and depth estimations: implemented on noisy sequences of synthetic images as well as on real data, they perform a more robust and accurate depth estimation. This approach is complementary to most methods employing state observers for range estimation, which uniquely concern single or isolated feature points.Comment: Submitte

Functional observers for motion control systems

This paper presents a novel functional observer for motion control systems to provide higher accuracy and less noise in comparison to existing observers. The observer uses the input current and position information along with the nominal parameters of the plant and can observe the velocity, acceleration and disturbance information of the system. The novelty of the observer is based on its functional structure that can intrinsically estimate and compensate the un-measured inputs (like disturbance acting on the system) using the measured input current. The experimental results of the proposed estimator verifies its success in estimating the velocity, acceleration and disturbance with better precision than other second order observers

Non-linear estimation is easy

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint

Smooth non linear high gain observers for a class of dynamical systems

High-gain observers are powerful tools for estimating the state of nonlinear systems. However, their design poses several challenges due to the need of dealing with phenomena such as peaking and chattering. To address these issues, we propose a differentiator operator design based on a non linear second order high-gain observer, which is suited to a class of dynamical systems. Our method includes a procedure to determine high gains in order to avoid chattering in the case of noise-free models, and cut-off frequency based gain design in the case of noisy measurements. Complementary, we suggest performing observability analyses to ensure a priori the feasibility of the estimation. The main strengths of our approach are its simplicity and robustness. We demonstrate the performance of the proposed method by applying it to two processes (chemical and biological).Xunta de Galicia | Ref. ED431F 2021/003MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-

Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers

[EN] This paper addresses the estimation of specific growth rate of microorganisms in bioreactors using sliding observers. In particular, a second-order sliding observer based on biomass concentration measurement is proposed. Differing from other proposals that only guarantee bounded errors, the proposed observer provides a smooth estimate that converges in finite time to the time-varying parameter. Stability is proved using a Lyapunov approach. The observer exhibits also robustness to process uncertainties since no model of the reaction is used for its design. In addition, the off-surface coordinate of the sliding observer is useful to determine the convergence time as well as to identify sensor faults and unexpected behaviors. Because of the structure of the output error injection, chattering phenomena of conventional sliding mode algorithms are substantially reduced. The features of the proposed observer are assessed by numerical and experimental data. (C) 2011 Elsevier Ltd. All rights reserved.This work was supported by the National University of La Plata (Project 11-1127), ANPCyT (PICT2007-00535) and CONICET (PIP112-200801-01052) of Argentina; the Technical University of Valencia (PAID-02-09 program and FPI-2009/21 grant), the CICYT (DPI2005-01180) and AECID (A/024186/09) of Spain: and by FEDER funds of the European Union.De Battista, H.; Picó, J.; Garelli, F.; Vignoni, A. (2011). Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers. Journal of Process Control. 21(7):1049-1055. https://doi.org/10.1016/j.jprocont.2011.05.008S1049105521

Constant Crunch Coordinates for Black Hole Simulations

We reinvestigate the utility of time-independent constant mean curvature foliations for the numerical simulation of a single spherically-symmetric black hole. Each spacelike hypersurface of such a foliation is endowed with the same constant value of the trace of the extrinsic curvature tensor, $K$. Of the three families of $K$-constant surfaces possible (classified according to their asymptotic behaviors), we single out a sub-family of singularity-avoiding surfaces that may be particularly useful, and provide an analytic expression for the closest approach such surfaces make to the singularity. We then utilize a non-zero shift to yield families of $K$-constant surfaces which (1) avoid the black hole singularity, and thus the need to excise the singularity, (2) are asymptotically null, aiding in gravity wave extraction, (3) cover the physically relevant part of the spacetime, (4) are well behaved (regular) across the horizon, and (5) are static under evolution, and therefore have no ``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate that we can stably evolve a single spherically-symmetric static black hole using this foliation. We wish to emphasize that this coordinatization produces $K$-constant surfaces for a single black hole spacetime that are regular, static and stable throughout their evolution.Comment: 14 pages, 9 figures. Formatted using Revtex4. To appear Phys. Rev. D 2001, Added numerical results, updated references and revised figure