STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.

SysteM of augmented reality for teaching kids: smartkids

As crianças do jardim de infância/pré-escola são um grupo de utilizadores muito especiais, uma vez que se encontram numa fase inicial das suas vidas onde têm de aprender a viver em sociedade, isto é, aprender a ouvir e respeitar as opiniões dos outros, partilhar os mesmos objectos e também a ajudar-se mutuamente. Este estudo mostra que através da utilização da tecnologia Realidade Aumentada, estas crianças são capazes de colaborar de uma forma espontânea suportada pela motivação, envolvimento e curiosidade. Descreve-se o design e a avaliação de um jogo de Realidade Aumentada, que consiste num sistema educativo para o ensino de crianças do pré-escolar. Este jogo permite que as crianças explorem conceitos tais como os animais e os meios onde vivem através de marcadores de Realidade Aumentada e de um tabuleiro de madeira. Estes marcadores consistem nas peças do jogo e através deles, as crianças podem manipular objectos virtuais em 3D. Foram realizados testes com diversas turmas de crianças em diferentes ambientes de aprendizagem, nomeadamente em escolas e num museu. Os resultados sugerem que o jogo é eficaz para obter níveis altos de concentração, motivação e colaboração entre as crianças, particularmente quando o feedback do jogo é fornecido de forma imediata. Os resultados mostram também que o jogo tem um impacto positivo sobre a experiência de aprendizagem das crianças.

Controle feedback de nível baseado em sensor de imagem aplicado ao equipamento misturador-decantador à inversão de fases (MDIF®)

The treatment of wastewaters contaminated with oil is of great practical interest and it is fundamental in environmental issues. A relevant process, which has been studied on continuous treatment of contaminated water with oil, is the equipment denominated MDIF® (a mixer-settler based on phase inversion). An important variable during the operation of MDIF® is the water-solvent interface level in the separation section. The control of this level is essential both to avoid the dragging of the solvent during the water removal and improve the extraction efficiency of the oil by the solvent. The measurement of oil-water interface level (in line) is still a hard task. There are few sensors able to measure oil-water interface level in a reliable way. In the case of lab scale systems, there are no interface sensors with compatible dimensions. The objective of this work was to implement a level control system to the organic solvent/water interface level on the equipment MDIF®. The detection of the interface level is based on the acquisition and treatment of images obtained dynamically through a standard camera (webcam). The control strategy was developed to operate in feedback mode, where the level measure obtained by image detection is compared to the desired level and an action is taken on a control valve according to an implemented PID law. A control and data acquisition program was developed in Fortran to accomplish the following tasks: image acquisition; water-solvent interface identification; to perform decisions and send control signals; and to record data in files. Some experimental runs in open-loop were carried out using the MDIF® and random pulse disturbances were applied on the input variable (water outlet flow). The responses of interface level permitted the process identification by transfer models. From these models, the parameters for a PID controller were tuned by direct synthesis and tests in closed-loop were performed. Preliminary results for the feedback loop demonstrated that the sensor and the control strategy developed in this work were suitable for the control of organic solvent-water interface level

LMI-based algorithm for strictly positive real systems with static output feedback

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Robust State-Derivative Feedback LMI-Based Designs for Linear Descriptor Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Design of a control system using linear matrix inequalities for the active vibration control of a plate

The study of algorithms for active vibration control in smart structures is an area of interest, mainly due to the demand for better performance of mechanical systems, such as aircraft and aerospace structures. Smart structures, formed using actuators and sensors, can improve the dynamic performance with the application of several kinds of controllers. This article describes the application of a technique based on linear matrix inequalities (LMI) to design an active control system. The positioning of the actuators, the design of a robust state feedback controller and the design of an observer are all achieved using LMI. The following are considered in the controller design: limited actuator input, bounded output (energy) and robustness to parametric uncertainties. Active vibration control of a flat plate is chosen as an application example. The model is identified using experimental data by an eigensystem realization algorithm (ERA) and the placement of the two piezoelectric actuators and single sensor is determined using a finite element model (FEM) and an optimization procedure. A robust controller for active damping is designed using an LMI framework, and a reduced model with observation and control spillover effects is implemented using a computer. The simulation results demonstrate the efficacy of the approach, and show that the control system increases the damping in some of the modes.

Observer-based state-feedback versus H-infinity output feedback control solved by LMI approach for applications in smart structures

This paper aims with the use of linear matrix inequalities approach (LMIs) for application in active vibration control problems in smart strutures. A robust controller for active damping in a panel was designed with piezoelectrical actuators in optimal locations for illustration of the main proposal. It was considered, in the simulations of the closed-loop, a model identified by eigensystem realization algorithm (ERA) and reduced by modal decomposition. We tested two differents techniques to solve the problem. The first one uses LMI approach by state-feedback based in an observer design, considering several simultaneous constraints as: a decay rate, limited input on the actuators, bounded output peak (output energy) and robustness to parametic uncertainties. The results demonstrated the vibration attenuation in the structure by controlling only the first modes and the increased damping in the bandwidth of interest. However, it is possible to occur spillover effects, because the design has not been done considering the dynamic uncertainties related with high frequencies modes. In this sense, the second technique uses the classical H. output feedback control, also solved by LMI approach, considering robustness to residual dynamic to overcome the problem found in the first test. The results are compared and discussed. The responses shown the robust performance of the system and the good reduction of the vibration level, without increase mass.

A simple feedback control for a chaotic oscillator with limited power supply

We proposed a simple feedback control method to suppress chaotic behavior in oscillators with limited power supply. The small-amplitude controlling signal is applied directly to the power supply system, so as to alter the characteristic curve of the driving motor. Numerical results are presented showing the method efficiency for a wide range of control parameters. Moreover, we have found that, for some parameters, this kind of control may introduce coexisting periodic attractors with complex basins of attraction and, therefore, serious problems with predictability of the final state the system will asymptote to. (c) 2006 Elsevier Ltd. All rights reserved.

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

Synchronization of the unified chaotic system and application in secure communication

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.