Necessary and sufficient condition for generalized passivity, passification and application to multivariable adaptive systems

Recently, a generalized passivity concept for linear multivariable systems was obtained which allows circumventing the restrictiveness of the usual passivity concept. The latter is associated with the classical SPR (Strictly Positive Real) condition whereas the new concept of passivity is associated with the so called WSPR condition and its advantage in multivariable systems is that it does not require a restrictive symmetry condition of SPR systems. As a result, it allows the design of multivariable adaptive control that, unlike some existing factorization approaches, does not imply in additional overparameterization of the adaptive controller. In this paper, we complete a previously established WSPR sufficient condition and prove that it is also necessary. We also propose some methods of passification by either premultiplying the system output tracking error vector or the system input vector by an adequate passifying matrix multiplier, so that the resulting input/output transfer function becomes WSPR. The efficiency of our proposals are illustrated by simulation utilizing a well known robotics adaptive visual servoing problem. © 2011 IFAC.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Systèmes de numération et automates

Let beta be an hyperbolic algebraic integer of modulus greater than 1. Lot A be a finite set of Q[beta] and D-beta = {(a(i), b(i))(igreater than or equal to0) is an element of (A x A)(N) \ Sigma(i=0)(infinity) a(i)beta(-i)}. We give a necessary and sufficient condition for D-beta to be sofic. As a consequence, we obtain a result due to Thurston (see Corollary 1). We also treat the case where the set of digits A is given by the greedy algorithm and study the connection with the beta-shift. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

COX23, a homologue of COX17, is required for cytochrome oxidase assembly

Deletion of reading frame YHR116W of the Saccharomyces cerevisiae nuclear genome elicits a respiratory deficiency. The encoded product, here named Cox23p, is shown to be required for the expression of cytochrome oxidase. Cox23p is homologous to Cox17p, a water-soluble copper protein previously implicated in the maturation of the Cu-A center of cytochrome oxidase. The respiratory defect of a cox23 null mutant is rescued by high concentrations of copper in the medium but only when the mutant harbors COX17 on a high copy plasmid. Overexpression of Cox17p by itself is not a sufficient condition to rescue the mutant phenotype. Cox23p, like Cox17p, is detected in the intermembrane space of mitochondria and in the postmitochondrial supernatant fraction, the latter consisting predominantly of cytosolic proteins. Because Cox23p and Cox17p are not part of a complex, the requirement of both for cytochrome oxidase assembly suggests that they function in a common pathway with Cox17p acting downstream of Cox23p.

Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

KT-invexity in optimal control problems

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

Breaking down the Fermi acceleration with inelastic collisions

The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341-348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. (c) 2006 Elsevier B.V. All rights reserved.

A class of multiobjective control problems

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

ANALISE FAMILIAL DO COMPORTAMENTO IN VITRO DOS MACROFAGOS HUMANOS FRENTE AO MYCOBACTERIUM LEPRAE

The lysogenic capacity of human macrophages facing M. leprae in vitro may be dependent on an important genetic component. Although the familial aggregation of the trait is demonstrated, this is a necessary but not sufficient condition to prove genetic influence. The data do not fit some simple genetic models (autosomal dominant or incompletely dominant gene; dominant or recessive sex-linked gene). The results obtained are consistent with the hypothesis that the macrophages' lysogenic capacity is mainly due to a major gene with variable expressivity. This hypothesis may be too simple to account for the whole variability detected and therefore must be considered a working hypothesis.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

A note on KKT-invexity in nonsmooth continuous-time optimization

We introduce the notion of KKT-inverity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.

Semigrupos de operadores lineares limitados: soluções Mild e Weak

Pós-graduação em Matemática - IBILCE