Gualberto Solis-Perales

A chaos-based communication scheme via robust asymptotic feedback

A communication scheme based on chaos synchronization via feedback is presented. The main idea is to construct an augmented dynamical system from the synchronization error system, which is itself uncertain. Dynamic output feedback is applied to perform synchronization in spite of transmitter/receiver mismatches. In this way, the transmitted message (which can be analog or digital) can be recovered. Two illustrative examples are presented. (1) The Chua oscillator is used to show that the message signal is recovered in spite of parametric transmitter/receiver mismatches. (2) Two second-order driven oscillators are presented to show that the message can be recovered in spite of a strictly different model, which results in different master/slave dynamics.

Complete Synchronization of Strictly Different Chaotic Systems

The criteria for complete synchronization of strictly different chaotic systems using feedback control are presented in this paper. Complete synchronization is achieved when all the states in the slave system are synchronous with the corresponding state in the master system. We illustrate that using a single input and single output control scheme, the synchronization of a class of strictly different systems is obtained in partial form. To overcome this problem we show that a multiple input and multiple output control scheme with an equal number of inputs and outputs than the order system is required in order to obtain the complete synchronization. This procedure is used to synchronize the Rossler and the Chen systems as an example. We also demonstrate that if the synchronization scheme considers less inputs and outputs, the partial-state synchronization is obtained.

Bilateral Teleoperation Control Without Velocity Measurements

Abstract This paper presents two controllers for a nonlinear bilateral teleoperation system that do not rely on velocity measurements. Under the reasonable assumptions that the human operator and the environment define passive maps from force to velocity, both controllers can ensure boundedness of velocities and position error. Moreover, if the human and environment forces are bounded, one of the controllers ensure velocity synchronization and the other velocity convergence to zero. Simulations, comparing the performance on free motion and interacting with a stiff wall, support the performance of the reported schemes.

Accounting the control effort to improve chaos suppression via robust adaptive feedback

This contribution deals with the optimisation of the chaos suppression via robust (low-parameterised) adaptive feedback. The robust adaptive feedback (RAF) has been proved to be capable of inducing the chaos suppression in face of uncertainties and exogenous disturbances. In this contribution the RAF scheme is accomplished with an optimal tuning scheme based on Riccatti equations. The underlying idea is to optimise the robust chaos suppression by accounting the control effort despite the saturation in electronic components. A finite horizon can be arbitrarily established by ensuring that the chaos suppression is achieved at established time. It should be noted that there is not exact convergence to the non-chaotic reference. As a matter of fact, only the suppression of the chaotic behaviour is aimed. An advantage is that the proposed scheme accounts the energy wasted by the controller and the closed-loop performance on suppression. Numerical and experimental results show the performance of the optimisation strategy.

Complex Discrete Dynamics and Its Structures in Bioinspired Systems

1 Departamento de Electronica, CUCEI, Universidad de Guadalajara, Avenida Revolucion 1500, CP 44430, Guadalajara, JAL, Mexico 2Division de Matematicas Aplicadas, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la Presa San Jose 2055, Colonia Lomas 4 Seccion, CP 78216, San Luis Potośi, SLP, Mexico 3 Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong

Robust Adaptive Synchronization in a Small Pacemaker Neuronal Ensemble

Abstract The synchronization of a pacemaker neuronal ensemble under the action of a robust and adaptive control command is studied herein. The ensemble corresponds to the pyloric central pattern generator of the stomatogastric ganglion of lobster. The desired dynamics is provided by means of an external neuron called the reference neuron and it is induced via a nonlinear controller. Such a controller is composed by a linearizing-like controller and a high gain estimator; the controller is able to counteract parameter variations, system uncertainties and external perturbations in the controlled system. Numerical simulations of the robust synchronization dynamics of the master neuron and the pacemaker neuronal ensemble are presented in order to corroborate the results.

A differential evolutionary method for solving a class of differential equations numerically

Abstract A method for solving differential equations using the differential evolutionary algorithm (DE) is presented in this contribution. In the case of differential equation is a polynomial function of its variables, the algorithm makes possible solution vectors evolve toward the best solution of the differential equation based on certain criteria, such as least squares or another error measure. In the case of non polynomial differential equations, the DE is applied in the context of variational methods. Numerical results for solving a segment of the Lorenz and van der Pol differential equations are provided.

Mutual Synchronization of Nonidentical Open Kinematic Chains

In this contribution we present the mutual synchronizationof an ensemble of robots with strictly differentarchitecture. The main idea is to achieve synchronizationin an group of robots composed by rotational-rotationaland rotational-prismatic architecture. The synchronization isachieved into the workspace, this is, the end position ofeach robot is equal to the rest of the robots. It impliesthat the resulting workspace is composed by the intersectionof the corresponding workspace. The mutual synchronizationis achieved by means of a PID controller and numericalsimulations are provided to illustrate the results.

Secure Multiple Signal Transmission Using Chaos Synchronization

Abstract In this contribution we present the secure transmission of several signals based on chaos synchronization. The idea is to transmit as many signals as system states in secure manner. It is required that the transmitted chaotic attractor does not change in order to maintain the security level. The method is based on the Multiple-Input and Multiple-Output (MIMO) control theory for nonlinear systems. Moreover the Transmitter and Receiver synchronizes in spite of the uncertainties in both systems. In this sense the secure communication scheme is robust. We illustrate the result using synchronization of similar systems.

Introduction to Chaos Control: An Interdisciplinary Problem

The foundational for chaos control problem is scientific as well as technological. In regard science, on the one hand, chaos control has two important contributions: (i) The controlled chaotic systems has allowed to understand that structured disorder and its entropy/information relationship extend the concept of determinism [1], [2] and (ii) departing from chaotification (inverse action of the chaos suppression) some questions have been opened on phenomena of the feedback dynamical systems [3]. Moreover, the chaos control impacts biomedical, life and engineering sciences; for example, it can be extended to control pathological rhythm in heart [4]. Now, regarding technological applications, the controlled chaotic systemsare important because of a desired frequency response can be induced. Nowadays, the scientific community has identified two problems in chaos control: suppression and synchronization. Among others, we can mention studies in physical devices (e.g., telescopes or lasers), biology/ecology (e.g., population dynamics or biodynamics) or biomedical systems (e.g., heart rhythm or brain activity). Thus, for instance, controlled current-modulation can be entered as excitation from a nonlinear circuit into semiconductors lasers by feeding back the laser frequency response (see Figure 1 in [5]). Henceforth, scientific community has taken possession of the challenge of exploring control techniques such that (i) a family of driving force can command classes of chaotic systems [6], (ii) the synthesis of mathematical expressions for the control force accounts the frequency response [7], and (iii) energy requirements by the control force are accounted (for example to avoid saturation or deterioration in control devices) [8]. In addition, the mathematical models of the driving force is desired to be simple and easy to implement experimentally. A simple form is the linear models of driving forces; which can be expressed in the frequency (Laplace) or time domain and they have been already used to suppress chaotic behavior [7], [9].