Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

A causal theory of error scores.

In Modern Test Theory, response variables are a function of a common latent variable that represents the measured attribute, and error variables that are unique to the response variables. While considerable thought goes into the interpretation of latent variables in these models (e.g., validity research), the interpretation of error variables is typically left implicit (e.g., describing error variables as residuals, i.e., as `whatever is unexplained by the model'). Yet, many psychometric assumptions are essentially assumptions about error and thus being able to reason about psychometric models requires the ability to reason about errors. We propose the causal theory of error as a framework that helps reasoning about errors in terms of the data-generating mechanism. In this framework, the error variable reflects all unique causes of the response variable that together with the latent variable determine the item responses. We show that different assumptions about error scores (1) imply different psychometric models, (2) have different implications for the chance experiment that underlies the notion of randomness in the model, and (3) have different implications for item bias and local homogeneity. In the causal theory of error, these assumptions concern the unique causes of the item response that may be person characteristics that have the sampling of people as their source of variability, or properties of the measurement circumstances that have the sampling of measurement occasions as their source of variability.

Attitude Control of Quadrotor Using PD Plus Feedforward controller on SO(3)

<p>This paper proposes a simple scheme of Proportional-Derivative (PD) plus Feedforward controller on SO(3) to control the attitude of a quadrotor. This controller only needs the measurement of angular velocity to calculate the exponential coordinates of the rotation matrix. With rotation matrix as an error variable of the controller, the simulation shows that the controller is able to drive the attitude of the quadrotor from hovering condition to desired attitude and from an attitude condition goes to the hovering condition, despite the system is disturbed. When the system is convergent, the rotation error matrix will be a 3x3 identity matrix.</p>

Uso de Análisis de Covarianza (ANCOVA) en investigación científica

Key words: ANCOVA, auxiliary variable, error reduction, statisticsAbstract. The basics of the ANalisis of COVAriance (ANCOVA) are given. The objectives and the application of ANCOVA are laid out. Techniques for the estimation of contrasts and for the control and reduction of the degree of error are discussed. The application of a simple ANCOVA using real data is highlighted. The application of this technique in fixing the auxiliary variable in experimentation is emphasized.Palabras clave: ANCOVA, Estadística, reducción de error, variable auxiliarResumen. Se presentan las bases del ANálisis de COVArianza (ANCOVA). Se manejan los propósitos y la aplicación de este método estadístico. Se discuten las técnicas para la estimación de los contrastes, el control y la disminución del grado de error. Se presentan un ANCOVA simple mediante un ejemplo de datos reales. Se enfatiza el papel de esta técnica estadística en fijar el efecto de la variable auxiliar en el experimento.

Quantification of Uncertainties in OCO-2 Measurements of XCO₂: Simulations and Linear Error Analysis

We present an analysis of uncertainties in global measurements of the column averaged dry-air mole fraction of CO2 ('XCO2') by the NASA Orbiting Carbon Observatory-2, ('OCO-2'). The analysis is based on our best estimates for uncertainties in the OCO-2 operational algorithm and its inputs, and uses simulated spectra calculated for the actual flight and sounding geometry, with measured atmospheric analyses. The simulations are calculated for land nadir and ocean glint observations. We include errors in measurement, smoothing, interference, and forward model parameters. All types of error are combined to estimate the uncertainty in XCO2 from single soundings, before any attempt at bias correction has been made. From these results we also estimate the 'variable error' which differs between soundings, to infer the error in the difference of XCO2 between any two soundings. The most important error sources are aerosol interference, spectroscopy, and instrument calibration. Aerosol is the largest source of variable error. Variable errors are usually

SYNCHRONIZATION CRITERIA FOR COUPLED CHAOTIC SYSTEMS WITH PARAMETER MISMATCHES

This paper studies synchronization between two linearly coupled non-autonomous chaotic systems with parameter mismatches. Based on Lyapunov's stability theory and Sylvester's criterion, some algebraic criteria are derived to synchronize the master and slave system with error bound. Besides, the largest synchronization error can be estimated analytically. Some numerical examples are presented to verify the effectiveness of these criteria. In the examples, the estimated largest synchronization error is compared with the evolution of the error variable, which further shows that the present techniques are effective.