A Robust Constrained Reference Governor Approach using Linear Matrix Inequalities

The purpose of this paper is to examine and provide a solution to the output reference tracking problem for uncertain systems subject to input saturation. As well-known, input saturation and modelling errors are very common problems at industry, where control schemes are implemented without accounting for such problems. In many cases, it is sometimes difficult to modify the existing implemented control schemes being necessary to provide them with external supervisory control approaches in order to tackle problems with constraints and modelling errors. In this way, a cascade structure is proposed, combining an inner loop containing any proper controller with an outer loop where a generalized predictive controller (GPC) provides adequate references for the inner loop considering input saturations and uncertainties. Therefore, the contribution of this paper consists in providing a state space representation for the inner loop and using linear matrix inequalities (LMI) to obtain a predictive state-vector feedback in such a way that the input reference for the inner loop is calculated to satisfy robust tracking specifications considering input saturations. Hence, the final proposed solution consists in solving a regulation problem to a fixed reference value subjected to a set of constraints described by several LMI and bilinear matrix inequalities (BMI). The main contribution of the paper is that the proposed solution is a non-linear setpoint tracking approach, that is, it is allowed that the system goes into saturation facing the problem of setpoint tracking instead of regulating to the origin. An illustrative numerical example is presented.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-01/0

The derivations of some evolution algebras

In this work we investigate the derivations of n−dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero. The spaces of derivations for evolution algebras with matrices of rank n−1 are described.Junta de Andalucía FQM-14

Threshold anomaly in non-central forces

The behaviour of the threshold anomaly for non-central potentials, which account for collective excitations in heavy-ion collisions, is investigated. It is shown that the non-central potentials should exhibit an energy dependence at energies in the vicinity of the Coulomb barrier. This energy dependence is, however, different from that of the elastic optical potential, occurring at lower energies. It if further shown that there are corrections to the traditional collective model such that, if the transition potential is expressed as the derivative of the optical potential, the corresponding deformation length will be complex and energy-dependent. Simple model calculations are presented.Dirección General de Investigaciones Científicas y Técnicas PB89-0636

Analytic description of the scattering of electrons by molecules

The scattering of electrons by molecules is considered. The structure of the molecule is described in terms of the vibron model, which is an algebraic approach to the description of rotational and vibrational molecular excitations. The dynamics of electron-molecule collision is discussed in terms of coupled-channel calculations, where we assume an isocentrifugal approximation. In the sudden limit, where the excitation energies of the molecule are neglected, the coupled-channel system decouples into eigenchannels. The scattering amplitudes of the eigenchannels, characterized by 1/r2 potentials, are obtained analytically. The resulting probabilities of excitation of the molecular states and the limiting values of the quasielastic cross sections are evaluated in the U(3) and the O(4) limits. A comparison of the results for the differential cross sections with experimental data and other calculations is made for LiF and KI.Dirección General de Investigación Científica y Técnica PB92-06

Programming Robosoccer agents by modelling human behavior

The Robosoccer simulator is a challenging environment for artificial intelligence, where a human has to program a team of agents and introduce it into a soccer virtual environment. Most usually, Robosoccer agents are programmed by hand. In some cases, agents make use of Machine learning (ML) to adapt and predict the behavior of the opposite team, but the bulk of the agent has been preprogrammed. The main aim of this paper is to transform Robosoccer into an interactive game and let a human control a Robosoccer agent. Then ML techniques can be used to model his/her behavior from training instances generated during the play. This model will be used later to control a Robosoccer agent, thus imitating the human behavior. We have focused our research on low-level behavior, like looking for the ball, conducting the ball towards the goal, or scoring in the presence of opponent players. Results have shown that indeed, Robosoccer agents can be controlled by programs that model human play.Publicad

Supervised data transformation and dimensionality reduction with a 3-layer multi-layer perceptron for classification problems

The aim of data transformation is to transform the original feature space of data into another space with better properties. This is typically combined with dimensionality reduction, so that the dimensionality of the transformed space is smaller. A widely used method for data transformation and dimensionality reduction is Principal Component Analysis (PCA). PCA finds a subspace that explains most of the data variance. While the new PCA feature space has interesting properties, such as removing linear correlation, PCA is an unsupervised method. Therefore, there is no guarantee that the PCA feature space will be the most appropriate for supervised tasks, such as classification or regression. On the other hand, 3-layer Multi Layer Perceptrons (MLP), which are supervised methods, can also be understood as a data transformation carried out by the hidden layer, followed by a classification/regression operation performed by the output layer. Given that the hidden layer is obtained after a supervised training process, it can be considered that it is performing a supervised data transformation. And if the number of hidden neurons is smaller than the input, also dimensionality reduction. Despite this kind of transformation being widely available (any neural network package that allows access to the hidden layer weights can be used), no extensive experimentation on the quality of 3-layer MLP data transformation has been carried out. The aim of this article is to carry out this research for classification problems. Results show that, overall, this transformation offers better results than the PCA unsupervised transformation method.This work has been supported by Agencia Estatal de Investigación (PID2019-107455RB-C22 /AEI/ 10.13039/501100011033), and Spanish Ministry of Science and Education under TIN2017-85727-C4-3-P (DeepBio) gran

Elastic Scattering of 6He on Heavy Targets at Coulomb Barrier Energies

Elastic cross sections for the scattering of 6He projectiles by 208Pb at 27 MeV have been studied. The data have been analyzed within the framework of the Optical Model using Saxon–Woods phenomenological form factors for both the real and imaginary parts of the nuclear potential. The elastic scattering data suggests the presence of a long range absorption mechanisms which might be related to the halo structure of 6He.Ministerio Ciencia y Tecnología FPA2002-04181- C04-04 y FPA2000-1592-C03-0

Coupled channel effects in the scattering of 6,7Li BY 58Ni

Using a single-particle description of 6,7Li and Woods-Saxon generated wavefunctions for 58Ni matter density distribution, the diagonal and transition densities are calculated. Folding these densities with the M3Y effective interaction, the coupling and diagonal potentials are obtained. Coupled channel calculations for 6,7Li on 58Ni at bombarding energies in a range from 12 to 74 MeV are performed. It is shown that the predictions of the coupled channel calculations are consistent with those of optical model calculations using folded potentials renormalized by a factor 0.6 in the entire range of energies

Geometric interpretation of the effect of the quadrupole force in the collisions of deformed nuclei

The effect of a quadrupole force on a set of degenerate states of a rotational band with arbitrary spin projection along the symmetry axis K is studied. Analytic expressions for the eigenvalues and eigenvectors are obtained in terms of a set of orthogonal polynomials. This is applied to the collision of a spherical nucleus with a deformed one in which the coupling to a given set of rotational states is allowed, ignoring excitation energies. The elastic S-matrix, transition amplitudes, and the fusion cross sections are obtained as a weighted average of the magnitudes corresponding to a set of definite orientations of the axis of the deformed nucleus with respect to the relative coordinate. That weighted average corresponds to approximate the extreme sudden result, consisting of an integral over all the orientations, by a generalized Gaussian quadratur