Juan Luis Mata-Machuca

Fault diagnosis viewed as a left invertibility problem

This work deals with the fault diagnosis problem, some new properties are found using the left invertibility condition through the concept of differential output rank. Two schemes of nonlinear observers are used to estimate the fault signals for comparison purposes, one of these is a proportional reduced order observer and the other is a sliding mode observer. The methodology is tested in a real time implementation of a three-tank system.

Synchronization of chaotic Liouvillian systems: An application to Chua's oscillator

In this paper we deal with the synchronization of chaotic oscillators with Liouvillian properties (chaotic Liouvillian system) based on nonlinear observer design. The strategy consists of proposing a polynomial observer (slave system) which tends to follow exponentially the chaotic oscillator (master system). The proposed technique is applied in the synchronization of Chuas circuit using Matlab-Simulink(R) and Matlab(R)-LMI programs. Simulation results are used to visualize and illustrate the effectiveness of Chuas oscillator in synchronization.

Monitoring in a predator-prey systems via a class of high order observer design

The goal of this work is the monitoring of the corresponding species in a class of predator-prey systems, this issue is important from the ecology point of view to analyze the population dynamics. The above is done via a nonlinear observer design which contains on its structure a high order polynomial form of the estimation error. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer, where it can be concluded that the performance of the observer is improved as the order of the polynomial is high. The proposed methodology is applied to a class of Lotka-Volterra systems with two and three species. Finally, numerical simulations present the performance of the proposed observer.

Asymptotic synchronization of the Colpitts oscillator

In this paper we deal with the observer-based asymptotic synchronization problem for a class of chaotic oscillators. Some results based on a differential algebraic approach are used in order to determine the algebraic observability of unknown variables. The strategy consists of proposing a slave system (observer) which tends to follow asymptotically the master system. The methodology is tested in the real-time asymptotic synchronization of the Colpitts oscillator by means of a proportional reduced order observer (PROO) of free-model type.

Synchronization of nonlinear fractional order systems

This paper deals with the master–slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order Rossler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.

Generalized Synchronization via the Differential Primitive Element

Abstract Generalized synchronization (GS) in nonlinear systems appears when the states of one system, through a functional mapping are equal to states of another. This mapping can be obtained if there exists a differential primitive element which generates a differential transcendence basis. We introduce a new definition of GS in nonlinear systems using the concept of differential primitive element. In this contribution, we investigate the GS problem when we have strictly different nonlinear systems and we consider that for both the slave and master systems only some states are available from measurements. The first component of the mapping is called differential primitive element and, in general, is defined by means of a linear combination of the known states and the inputs of the system. Furthermore, we design a new dynamical feedback controller able to achieve complete synchronization in the coordinate transformation systems and GS in the original coordinates. These particular forms of GS are illustrated with numerical results of well-known chaotic benchmark systems.

A new observer for nonlinear fractional order systems

In this work an observer structure for a certain class of nonlinear fractional order systems is proposed. For solving this task we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the observer system. We apply our proposals in the master-slave synchronization problem, where the coupling signal is viewed as output and the slave system is regarded as observer (the slave is requested to recover the unknown state trajectories of the master). Finally, as numerical example we consider a fractional order Rössler hyperchaotic system and by means of some simulations we show the effectiveness of the suggested approach.

Fault diagnosis via a polynomial observer

The fault diagnosis problem of a class of nonlinear systems based on a differential approach is used to determine fault diagnosability with the minimum number of measurements from the system. In order to reconstruct the faults on the system, a polynomial observer is proposed, which includes in its structure corrections terms of high order. Another two schemes of nonlinear observers are used for reconstructing the faults for comparison purposes, one of them being a reduced order observer and the other a sliding mode observer. The approach was tested in a real-time experimental setting Amira DTS-200.

On the Observability for a Class of Nonlinear (Bio)chemical Systems

In this work the observability properties for a class of nonlinear systems is presented, by considering linear, geometric and algebraic approaches. The observability conditions for state variables, unstructured uncertainties and detectable states are considered for a class of nonlinear systems related with several (bio)-chemical reacting processes. The considered examples are related with (bio)-chemical continuous reactors and a metabolic model, where their observability properties are analyzed. A comparison of the corresponding results is done, showing the suitability of each approach.

Uniformly Bounded Error Estimator for Bioprocess with Unstructured Cell Growth Models

In this paper, we proposed a uniformly bounded error estimator for a common class of bioreactor models. The biomass and other products are estimated by means of substrate concentration measurements employing the characteristics of the unstructured cell growth models, which are linearly dependent. The estimation methodology is based on a suitable change of variable which allows generating artificial variables to infer the remaining mass concentrations constructing a differential-algebraic structure. The proposed methodology is applied to a class of Monod unstructured kinetic model with success. Some remarks about the convergence characteristics of the proposed estimator are given and numerical simulations show its satisfactory performance.