Derivative observations in Gaussian Process models of dynamic systems

Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1)It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training size - traditionally a problem for Gaussian process models

Divide and conquer identification using Gaussian process priors

We investigate the reconstruction of nonlinear systems from locally identified linear models. It is well known that the equilibrium linearisations of a system do not uniquely specify the global dynamics. Information about the dynamics near to equilibrium provided by the equilibrium linearisations is therefore combined with other information about the dynamics away from equilibrium provided by suitable measured data. That is, a hybrid local/global modelling approach is considered. A non-parametric Gaussian process prior approach is proposed for combining in a consistent manner these two distinct types of data. This approach seems to provide a framework that is both elegant and powerful, and which is potentially in good accord with engineering practice

Observer based synchronization of chaotic systems

We show that-the synchronization of chaotic systems can be achieved by using the observer design techniques which are widely used in the control of dynamical systems. We show that local synchronization is possible under relatively mild conditions and global synchronization is possible if the chaotic system can be transformed into a special form. We also give some examples including the Lorenz, the Rössler systems, and Chua's oscillator which are known to exhibit chaotic behavior, and show that in these systems synchronization by using observers is possible

Observer based chaotic message transmission

We consider observer based synchronization of continuous-time chaotic systems. We present two message transmission schemes for such systems. The first one is based on chaotic masking and modulation, and the second one is based on only chaotic modulation. We show that in these schemes, the message may be recovered under certain conditions. We show that the proposed schemes are robust with respect to noise and parameter mismatch. We also present some simulation results

Observer-based control of a class of chaotic systems

We consider the control of a class of chaotic systems, which covers the forced chaotic oscillators. We focus on two control problems. The first one is to change the dynamics of the system to a new one which exhibits a desired behavior, and the second one is the tracking problem, i.e., to force the solutions of the chaotic system to track a given trajectory. To solve these problems we use observers which could be used to estimate the unknown states of the system to be controlled. We apply the proposed method to the control of Duffing equation and the Van der Pol oscillator and present some simulation results. © 2001 Elsevier Science B.V

Characterization of a benzoic acid modified glassy carbon electrode expressed quantitatively by new statistical parameters

The main aim of this study is to characterize the nanosurface of the benzoic acid modified glassy carbon (GC) electrode by using a new statistical approach. In this study, the electrode surfaces were modified by cyclic voltametry in the potential range of +0.4 and -0.8 V at a scan rate 200 mV s-1 for four cycles versus Ag/Ag+ electrode in acetonitrile containing 0.1 M tetrabutylammonium tetraflouroborate (TBATFB). FT-IR spectra of the surface modifier molecules in both solid (GC and nanofilm (GC-benzoic acid)) forms were recorded in the spectral range 600-4000 cm-1. The FT-IR spectra of p-aminobenzoic acid were obtained by using KBr pellets. The above FT-IR spectra of both GC and its nanofilm with benzoic acid were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of GC-benzoic acid. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. © 2008 Elsevier B.V. All rights reserved

Analysis of a nanofilm of the mercaptophenyl diazonium modified gold electrode within new statistical parameters

The main aim of this study is to characterize the nanosurface of the mercaptophenyl diazonium modified gold (Au) surface by a new statistical approach. In this study the gold electrode surfaces were self-assembled in ethyl alcohol by 1.0 mM mercaptophenyl diazonium. FT-IR spectra of the surface modifier molecules in both solid and nanofilm of mercaptophenyl diazonium (MCP-Au) forms were recorded in the spectral range of 600-4,000 cm-1. The FT-IR spectra of solid mercaptophenyl diazonium tetrafluoroborate salt were obtained by using KBr pellets. The above FT-IR spectra of both bare Au and its nanofilm of mercaptophenyl diazonium were processed by new statistical approach to reach optimal smoothing trend for the characterization of the modified electrode surface consisting of the nanofilm of gold-mercaptophenyl diazonium. In the frame of new statistical approach all measured spectra have been 'read' in terms of a set of universal statistical parameters. These new parameters help to establish the statistical proximity of the smoothed spectra compared and give a possibility to classify the measured spectra in accordance with new set of statistical and robust quantitative values. Besides, there is a possibility to receive the relative fluctuations and the smoothed spectra of the second order. So, thanks to new approach we do not loose any measured information: the smoothed spectra and accompanied them noise (relative fluctuations) can be analyzed separately for detection of possible influence of predominant external factors that can be essential for this type of measurements. Copyright © 2010 American Scientific Publishers All rights reserved

Application of the linear principle for the strongly-correlated variables: Calculations of differences between spectra

In this paper the authors suggest a new method of detection of possible differences between similar near infrared (NIR) spectra based on the self-similar (fractal) property. This property is a general characteristic that belongs to a wide class of the strongly-correlated systems. As an example we take a set of NIR spectra measured for three systems: (1) glassy carbon (GC) electrodes, (2) GC electrodes affected by azobenzene (AB) substance and finally (3) films (AB-FILM). Besides the physical model that should describe the intrinsic properties of these substances we found the fitting function that follow from the linear principle for the strongly-correlated variables. This function expressed in the form of linear combination of 4 power-law functions describes with the high accuracy the integrated curves that were obtained from the averaged values of the initially measured spectra. The nine fitting parameters can be considered as the quantitative "finger prints" for detection of the differences between similar spectra. Besides this result we established the self-similar behavior of the remnant functions. In other words, the difference between the initially integrated function and its fitting function can be expressed in the form of linear combinations of periodical functions having a set of frequencies following to relationship ω(k)=ω0ξk, where the initial frequency ω0 and scaling factor ξ are determined by the eigen-coordinates method. This behavior in the NIR spectra was discovered in the first time and physical reasons of such behavior merit an additional research. © 2011

Analysis of the effect of potential cycles on the reflective infrared signals of nitro groups in nanofilms: Application of the fractional moments statistics

The effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms was studied for the statistical characterization of nitrobenzene (NB) and nitroazobenzene (NAB)-modified glassy carbon (GC) surfaces. Both NB and NAB nanofilms were obtained by the electrochemical reduction of the diazonium tetrafluoroborate salts in acetonitrile using cyclic voltammetry (CV). The modified surfaces were denoted as GC-(NB)n and GC-(NAB)n, respectively, where n indicates the number of CV cycles performed during modification. Reflective IR signals of the normalized NB and NAB nanofilms and GC were used for the quantitative evaluation of the effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms. The detection and quantitative reading of the influence of number of CV cycles were realized in the frame of a new error controllable approach that was applied for analysis of all available set of data. This approach includes in itself the following basic steps: (a) the procedure of the division (normalization) on the GC spectra, (b) the comparison of the smoothed spectra for their statistical proximity in the frame of the statistics of the fractional moments, (c) extraction of possible calibration parameters for possible calibration of the normalized spectra with respect to the number of CV cycles. These three basic steps are becoming effective for detection of the influence of some external factors. In our case it is important to detect the influence of the factor n characterizing CV cycles