Controllability distributions and systems approximations: a geometric approach

Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the result

Controllability distributions and systems approximations: a geometric approach

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. The relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximatio

One-shot 3d surface reconstruction from instantaneous frequencies: solutions to ambiguity problems

Phase-measuring profilometry is a well known technique for 3D surface reconstruction based on a sinusoidal pattern that is projected on a scene. If the surface is partly occluded by, for instance, other objects, then the depth shows abrupt transitions at the edges of these occlusions. This causes ambiguities in the phase and, consequently, also in the reconstruction.\ud This paper introduces a reconstruction method that is based on the instantaneous frequency instead of phase. Using these instantaneous frequencies we present a method to recover from ambiguities caused by occlusion. The recovery works under the condition that some surface patches can be found that are planar. This ability is demonstrated in a simple example. \u

Nonlinear disturbance decoupling and linearization: a partial interpretation of integral feedback

The relation between the solvability of the disturbance decoupling problem for a nonlinear system and its linearization around a working point is investigated. It turns out that generically the solvability of the disturbance decoupling via regular dynamic state feedback is preserved under linearization. This result gives a partial interpretation of introducing integral action in classical PID-control applied to nonlinear systems. The theory is illustrated by means of a worked example

Outcomes in patients with chronic uveitis: which factors matter to patients? A qualitative study

PURPOSE: Outcome measurements currently used in chronic uveitis care fail to cover the full patient perspective. The aim of this study is to develop a conceptual model of the factors that adult patients with chronic uveitis consider to be important when evaluating the impact of their disease and treatment. METHODS: A qualitative study design was used. Twenty chronic uveitis patients were recruited to participate in two focus groups. Data were transcribed verbatim and analysed using thematic analysis in ATLAS.ti. RESULTS: Coding of the transcripts resulted in a total of 19 codes divided over five themes: 1) disease symptoms and treatment; 2) diagnosis and treatment process; 3) impact on daily functioning; 4) emotional impact; and 5) treatment success factors. CONCLUSION: The conceptual model resulting from this study can contribute to the development of future uveitis specific measures in adults

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Decoupling problems around a trajectory: from linearity to nonlinearity

Given a nonlinear control system for which an admissible state trajectory is specified, we solve approximately the input output decoupling problem around this nominal trajectory. An approximate solution for this problem is obtained by dealing with the linearized system along this trajectory. An exact solution to the input output decoupling problem for the linearization is shown to be an approximate solution to the input output decoupling problem around the nominal trajectory for the original nonlinear system. In a similar way, we provide an approximate solution to the disturbance decoupling problem around a specified trajectory of the nonlinear system. The nonlinear model of a two link robot manipulator is used to illustrate the results on input output decoupling

Adsorption kinetics of DowexTM OptiporeTM L493 for the removal of the furan 5-hydroxymethylfurfural from sugar

BACKGROUND: Recently much research has been focused on the production and refinery of biobased fuels. The production of biofuels derived from lignocellulosic biomass is recognized as a promising route to produce biobased fuels responsibly. Often, product streams (e.g. glucose) still contain small amounts of undesired components (e.g. furans such as HMF). This study focuses on the removal of furans produced during the fermentation. In earlier work, styrene based resins have been identified as promising materials for this separation. In this work the kinetic properties of the most promising resin: DowexTM OptiporeTM L493 are studied. RESULTS: The diffusion coefficient of 5 mg L-1 HMF was ∼8×10-12 m2 s-1 in water and 3.0×10-12 m2 s-1 in a glucose solution. The reduced diffusion coefficient in the particle when glucose is present is caused by the higher viscosity of the glucose solution and it indicates that diffusion is controlled by surface and pore diffusion. The breakthrough curves of HMF on Optipore showed that the column is very efficient under conditions of interest. CONCLUSION: This study shows that Optipore is a much more efficient resin for HMF removal than currently used resins. Its fast kinetics and capacity make it possible to efficiently remove HMF from glucose solutions