H-infinity control design for time-delay linear systems: a rational transfer function based approach

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

Stability of multistep second derivative methods for integro-differential equations

The stability of multistep second derivative methods for integro-differential equations is examined through a test equation which allows for the construction of the associated characteristic polynomial and its region of stability (roots in the unit circle) at a proper parameter space. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Thermodynamic analysis of a non linear lattice

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

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier B.V. All rights reserved.

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

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

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Optimal and sub-optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright (C) 2001 John Wiley & Sons, Ltd.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Dehydration and volatilization non isothermic kinetic of the solid state aluminium 8-hydroxyquinolinate

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

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).

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.