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.

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimal pest control problem in population dynamics

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov 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. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 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.

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

Quality of service control for rt-VBR connections in ATM networks

Nowadays, networks must support applications such as: distance learning, electronic commerce, access to Internet, Intranets and Extranets, voice over IP (Internet Protocol) and many others. These new applications, employing data, voice, and video traffic, require high bandwidth and Quality of Service (QoS). The ATM (Asynchronous Transfer Mode) technology, together with dynamic resource allocation methods, offers network connections that guarantee QoS parameters, such as minimum losses and delays. This paper presents a system that uses Network Management Functions together with dynamic resource allocation for provision of the end-to-end QoS parameters for rt-VBR connections.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

The neuranatomical basis of central control of cardiorespiratory interactions in vertebrates

It seems that a dual location for vagal preganglionic neurones (VPNs) has important functional correlates in all vertebrates. This may be particularly the case with the central control exerted over the heart by cardiac VPNs (CVPNs). About 30 % of VPNs but up to 70 % of CVPNs are in the nucleus ambiguus (NA) of mammals. There is a similar proportional representation of VPNs between the major vagal nuclei in amphibians and turtles but in fish and crocodilians; the proportion of VPNs in the NA is closer to 10% and in some lizards and birds it is about 5%. However, the CVPNs are distributed unequally between these nuclei so that 45 % of the CVPNs are located in the NA of the dogfish, and about 30% in the NA of Xenopus and the duck. This topographical separation of CVPNs seems to be of importance in the central control of the heart. Cells in one location may show respiration-related activity (e.g those in the dorsal vagal nucleus (DVN) of dogfish and in the NA of mammals) while cells in the other locations do not. Their different activities and separate functions will be determined by their different afferent inputs from the periphery or from elsewhere in the CNS, which in turn will relate to their central topography. Thus, CVPNs in the NA of mammals receive inhibitory inputs from neighbouring inspiratory neurones, causing respiratory sinus arrythmia (RSA), and the CVPNs in the DVN of the dogfish may generate cardiorespiratory synchrony (CRS).

Sufficients conditions for analysis of extrema in the step-response of the linear control systems

This note deals whith the problem of extrema which may occur in the step-response of a stable linear system with real zeros and poles. Some simple sufficients conditions and necessary conditions are presented for analyses when zeros located between the dominant and fastest pole does not cause extrema in the step-response. These conditions require knowledge of the pole-zero configuration of the corresponding transfer-function.

Expressed sequence tags from Atta laevigata and identification of candidate genes for the control of pest leaf-cutting ants.

Leafcutters are the highest evolved within Neotropical ants in the tribe Attini and model systems for studying caste formation, labor division and symbiosis with microorganisms. Some species of leafcutters are agricultural pests controlled by chemicals which affect other animals and accumulate in the environment. Aiming to provide genetic basis for the study of leafcutters and for the development of more specific and environmentally friendly methods for the control of pest leafcutters, we generated expressed sequence tag data from Atta laevigata, one of the pest ants with broad geographic distribution in South America. Results: The analysis of the expressed sequence tags allowed us to characterize 2,006 unique sequences in Atta laevigata. Sixteen of these genes had a high number of transcripts and are likely positively selected for high level of gene expression, being responsible for three basic biological functions: energy conservation through redox reactions in mitochondria; cytoskeleton and muscle structuring; regulation of gene expression and metabolism. Based on leafcutters lifestyle and reports of genes involved in key processes of other social insects, we identified 146 sequences potential targets for controlling pest leafcutters. The targets are responsible for antixenobiosis, development and longevity, immunity, resistance to pathogens, pheromone function, cell signaling, behavior, polysaccharide metabolism and arginine kynase activity. Conclusion: The generation and analysis of expressed sequence tags from Atta laevigata have provided important genetic basis for future studies on the biology of leaf-cutting ants and may contribute to the development of a more specific and environmentally friendly method for the control of agricultural pest leafcutters.