Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

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

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

OUTPUT CONTROL WITH DYNAMIC COMPENSATORS AND STRICTLY POSITIVE REAL SYSTEMS

We present new results on the output control of uncertain dynamical systems. The design method uses dynamical compensators to turn the compensated plant into a strictly positive real system, and then chooses the control law-for example, a sliding mode control. This result is compared with another result from the literature which uses static compensators. An example is presented where the control with dynamic compensation works while a static compensation does not.

On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Semisolid systems containing propolis for the treatment of periodontal disease: In vitro release kinetics, syringeability, rheological, textural, and mucoadhesive properties

Formulations containing poloxamer 407 (P407), carbopol 934P (C934P), and propolis extract (PE) were designed for the treatment of periodontal disease. Gelation temperature, in vitro drug release, rheology, hardness, compressibility, adhesiveness, mucoadhesion, and syringeability of formulations were determined. Propolis release from formulations was controlled by the phenomenon of relaxation of polymer chains. Formulations exhibited pseudoplastic flow and low degrees of thixotropy or rheopexy. In most samples, increasing the concentration of C934P content significantly increased storage modulus (G'), loss modulus (G ''), and dynamic viscosity (n') at 5 degrees C, G '' exceeded G'. At 25 and 37 degrees C, n' of each formulation depended on the oscillatory frequency. Formulations showed thermoresponsive behavior, existing as a liquid at room temperature and gel at 34-37 degrees C. Increasing the C934P content or temperature significantly increased formulation hardness, compressibility, and adhesiveness. The greatest mucoadhesion was noted in the formulation containing 15% P407 (w/w) and 0.25% C934P (w/w). The work of syringeability values of all formulations were similar and very desirable with regard to ease of administration. The data obtained in these formulations indicate a potentially useful role in the treatment of periodontitis and suggest they are worthy of clinical evaluation. (c) 2007 Wiley-Liss, Inc.

A high dynamic range method for the direct readout of a dynamic phase change in homodyne interferometers

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

Stability analysis of power systems described with detailed models by automatic method

The power system stability analysis is approached taking into explicit account the dynamic performance of generators internal voltages and control devices. The proposed method is not a direct method in the usual sense since conclusion for stability or instability is not exclusively based on energy function considerations but it is automatic since the conclusion is achieved without an analyst intervention. The stability test accounts for the nonconservative nature of the system with control devices such as the automatic voltage regulator (AVR) and automatic generation control (AGC) in contrast with the well-known direct methods. An energy function is derived for the system with machines forth-order model, AVR and AGC and it is used to start the analysis procedure and to point out criticalities. The conclusive analysis itself is made by means of a method based on the definition of a region surrounding the equilibrium point where the system net torque is equilibrium restorative. This region is named positive synchronization region (PSR). Since the definition of the PSR boundaries have no dependence on modelling approximation, the PSR test conduces to reliable results. (C) 2008 Elsevier Ltd. All rights reserved.

Dynamic stationary response of reinforced plates by the boundary element method

A direct version of the boundary element method (BEM) is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs). Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state ( membrane) and for the out-of-plane state ( bending). These uncoupled systems are joined to formamacro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs). A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM).

Electrofluid dynamic (EFD) energy conversion in gas flows with suspended nanoparticles

This work presents simulations of the Electrofluid Dynamic energy conversion process in slender channel devices having very small particles (in both micro and nano scales) as charge carriers. Solutions are discussed for a system composed by coupled differential equations, which includes the equation for the total current along the channel, the equations for total energy and momentum of the mixture (gas and solid particles), the continuity equation and the equations for energy and momentum of a single particle. Results for suspended particles of higher diameters have been previously published in the Literature, but the simulations here presented exhibit an appreciable increase in the values for output currents.

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Carbon dioxide efflux in a rhodic hapludox as affected by tillage systems in southern Brazil

Os solos agrícolas podem atuar como dreno ou fonte de C atmosférico, dependendo do sistema de manejo adotado. Este estudo foi desenvolvido em experimento de longa duração (22 anos), durante o período de 30 dias do outono, com o objetivo de avaliar o impacto de sistemas de preparo de solo (preparo convencional-PC e plantio direto-PD) nas emissões de C-CO2 de um Latossolo Vermelho distrófico, em Cruz Alta, RS. As emissões de C-CO2 do solo foram avaliadas com câmaras dinâmica (Flux Chamber 6400-09, Licor) e estática (com captação em solução alcalina), imediatamente após a colheita da soja. A temperatura e a umidade do solo foram registradas, concomitantemente com as emissões de C-CO2, por meio de sensor de temperatura e TDR manual, respectivamente, integrantes do Licor-6400. Estimou-se que, em 30 dias, uma quantidade equivalente a menos de 30 % do C aportado pelos resíduos de soja foi emitida na forma de C-CO2. As emissões de C-CO2 no solo em PD foram similares às emissões do solo em PC, independentemente do tipo de câmara utilizada. Diferenças entre sistemas de preparo quanto à emissão de C-CO2, avaliadas com a câmara dinâmica, foram verificadas somente a curto prazo (leituras diárias), com o PD apresentando maiores emissões do que o PC no início do período experimental e menores no final. A câmara dinâmica foi mais eficiente do que a estática em captar as alterações das emissões de C-CO2 em função da variação da temperatura e a porosidade preenchida por água (PPA) no solo em PD, as quais explicaram 83 e 62 % das emissões de C-CO2, respectivamente. O fator Q10, que avalia a sensibilidade da emissão de C-CO2 à temperatura do solo, foi estimado em 3,93, indicando alta sensibilidade da atividade microbiana à temperatura do solo durante o outono. As emissões de C-CO2 registradas no solo em PD com a câmara estática foram correlacionadas às da câmara dinâmica, porém com valores subestimados em relação àquela notadamente nos maiores valores de fluxo. em condições de baixa temperatura e PPA, o preparo de solo induziu limitado incremento de emissão de C-CO2.