On algebraic time-derivative estimation and deadbeat state reconstruction

This note places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown that the algebraic method can in a sense be seen as a special case of deadbeat state estimation based on the reconstructibility Gramian of the considered system.Comment: Maple-supplements available at https://www.tu-ilmenau.de/regelungstechnik/mitarbeiter/johann-reger

A Deadbeat Observer for Two and Three-dimensional LTI Systems by a Time/Output-Dependent State Mapping

The problem of deadbeat state reconstruction for non-autonomous linear systems has been solved since several decades, but all the architectures formulated since now require either high-gain output injection, which amplifies measurement noises (e.g., in the case of sliding-mode observers), either state augmentation, which yields a non-minimal realization of the deadbeat observer (e.g., in the case of integral methods and delay-based methods). In this context, the present paper presents, for the first time, a finite-time observer for continuous-time linear systems enjoying minimal linear-time-varying dynamics, that is, the observer has the same order of the observed system. The key idea behind the proposed method is the introduction of an almost-always invertible time/output-dependent state mapping which allows to recast the dynamics of the system in a new observer canonical form whose initial conditions are known

Volterra's kernels-based finite-time parameters estimation of the Chua system

In this work, the unknown set of parameters of the Chua system is recovered under the hypothesis that the voltages of the capacitors are available. The system is shown to be algebraically observable and identifiable with respect to the chosen outputs. Focusing on the differential equations, the Volterra kernel-based approach is used to perform an estimation without the uncertainty of the unmeasurable derivatives and the unknown initial conditions

Kernel-based simultaneous parameter-state estimation for continuous-time systems

In this note, the problem of jointly estimating thestate and the parameters of continuous-time systems is addressed.Making use of suitably designed Volterra integral operators,the proposed estimator does not need the availability of time-derivatives of the measurable signals and the dependence ontheunknown initial conditions is removed. As a result, the estimatesconverge to the true values in arbitrarily short time in noise-freescenario. In the presence of bounded measurement and processdisturbances, the estimation error is shown to be bounded. Thenumerical implementation aspects are dealt with and extensivesimulation results are provides showing the effectivenessof theestimator

Algebraic Time-derivative Estimation in the Context of Reconstructibility

Das sogenannte algebraische Verfahren zur Schätzung von Zeitableitungen gemessener Signale, wie von Fliess und Sira Ramírez vorgeschlagen, wird aus klassischen Resultaten der Optimalschätzung hergeleitet. Insbesondere wird anhand einfacher Rechnungen gezeigt, wie sich das algebraische Verfahren als ein Sonderfall der Zustandsrekonstruktion mit Hilfe von Rekonstruierbarkeits-Gramschen ergibt. Abschließend werden Verbindungen zu weiteren Verfahren, wie Least-Squares und dem Kalman-Filter, hergestellt und Implikationen für die Praxis erörtert. The so-called algebraic approach to time-derivative estimation of measurement signals, proposed by Fliess and Sira Ramírez, is developed out of classical results from optimal estimation theory. By means of simple calculations it is shown that the algebraic method may be obtained as a special case of state reconstruction using reconstructibility Gramians. The paper concludes with links to further estimation methods, as least-squares estimation and Kalman-filtering, and points out practical implications. Copyright © 2009 Oldenbourg Wissenschaftsverlag Gmb

An algebraic observer for leak detection and isolation in plastic pipelines

In the continuation of authors' studies on leak diagnosis in pipelines, a new model-based Leak Detection and Isolation (LDI) algorithm is designed. This system only uses measures of flow and pressure coming from sensors placed at the ends of a pipeline. The present approach is based on a finite nonlinear pipeline model, and extended with variables related to the leak. On this basis, the purpose here is to investigate the use of a so-called algebraic observer to estimate the leak position and its magnitude. The corresponding observer design is thus presented, and its performances are illustrated both with simulation results, and experimental ones, with data taken from a real pipeline prototype.Consejo Nacional de Ciencia y TecnologíaInstitut Universitaire de FranceUniversidad Nacional de Colombi