Weak dual residuations applied to tropical linear equations

An extension to an algorithm of R.A. Cuninghame-Green and K. Zimmermann for solving equations with residuated functions is presented. This extension relies on the concept of weak residuation and in the so-called “strong property”. It is shown that a contextualization of this method to tropical linear equations, which will be denoted as Primal Method (in contrast with the Dual Method, another algorithm described in literature), generates a non-decreasing sequence which converges to the smallest solution in a special semimodule. It is also shown the connections of this method with previously published works

On Max-Plus Linear Dynamical System Theory: The Regulation Problem

A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “Max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus regulation problem”. In this context we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems. The obtained controller is a simple linear static state feedback and can be computed using efficient pseudo-polynomial algorithms. Simulation results will illustrate the applicability of the proposed methodology

On max-plus linear dynamical system theory: the observation problem

In this paper, we are interested in the general problem of estimating a linear function of the states for a given Max-Plus linear dynamical system. More precisely, using only the current and past inputs/outputs of the system, we want to construct a sequence that converges in a finite number of steps to the value given by a linear function of the states, for all initial conditions of the system. We provide necessary and sufficient conditions to solve this general problem. We also define and study a Max-Plus version of the well-known Luenberger observer, which is a subclass of the general problem that we are interested in, and we also provide necessary and sufficient conditions to solve this particular problem of observer synthesis. Finally, we show that there are important connections between results in the Max-Plus domain and associated results in the standard linear systems theory

On the Steady State Control of Timed Event Graphs with Firing Date Constraints

Two algorithms for solving a specific class of steadystate control problems for Timed Event Graphs are presented. In the first, asymptotic convergence to the desired set is guaranteed. The second algorithm, which builds on from the recent developments in the spectral theory of min-max functions, guarantees Lyapunov stability since the distance between the actual state and the desired set never increases. Simulation results show the efficiency of the proposed approach in a problem of moderate complexity

The oxygen uptake slow component at submaximal intensities in breaststroke swimming

The present work proposed to study the oxygen uptake slow component (VO2 SC) of breaststroke swimmers at four different intensities of submaximal exercise, via mathematical modeling of a multi-exponential function. The slow component (SC) was also assessed with two different fixed interval methods and the three methods were compared. Twelve male swimmers performed a test comprising four submaximal 300 m bouts at different intensities where all expired gases were collected breath by breath. Multi-exponential modeling showed values above 450 ml·min-1 of the SC in the two last bouts of exercise (those with intensities above the lactate threshold). A significant effect of the method that was used to calculate the VO2 SC was revealed. Higher mean values were observed when using mathematical modeling compared with the fixed interval 3rd min method (F=7.111; p=0.012; η2=0.587); furthermore, differences were detected among the two fixed interval methods. No significant relationship was found between the SC determined by any method and the blood lactate measured at each of the four exercise intensities. In addition, no significant association between the SC and peak oxygen uptake was found. It was concluded that in trained breaststroke swimmers, the presence of the VO2 SC may be observed at intensities above that corresponding to the 3.5 mM-1 threshold. Moreover, mathematical modeling of the oxygen uptake on-kinetics tended to show a higher slow component as compared to fixed interval methods.info:eu-repo/semantics/publishedVersio

Evolution in swimming "science" research

Swimming seems to be one of the sports more studied . More than one decade ago, Clarys (1996) made an content analysis of the research about swimming. However, in these last 13 years several developments happened in the aquatic activities

An Observer for Tropical Linear Event-Invariant Dynamical Systems

This paper presents a sufficient condition to solve the observation problem in tropical linear event-invariant dynamical systems, where a linear functional of the states can be observed in a finite number of steps using only the information from inputs and outputs. Using the residuation theory, this solvability condition can be easily implemented in polynomial time. Moreover, the main results are applied to state feedback control using only the observed states based on the measurements of the original states in the system. Furthermore, the main results are implemented in the perturbation observation problem for tropical linear event-invariant dynamical systems, where the system matrices are perturbed in intervals.

Evolution on Swimming Science Research: content analysis of the “Biomechanics and Medicine in Swimming” Proceedings Books from 1971 to 2006

Swimming seems to be one of the sports more studied . More than one decade ago, Clarys (1996) made an content analysis of the research about swimming. However, in these last 13 years several developments happened in the aquatic activities