Víctor Blanco

Design of Embedded DSP-Based Fuzzy Controllers for Autonomous Mobile Robots

Fuzzy controllers are used in many applications because of their rapid design by translating heuristic knowledge, robustness against perturbations, and smoothness in the control action. However, they require parallel processing and special operators (such as fuzzification or defuzzification) which are not available in standard digital signal processors (DSPs), thus complicating their direct implementation. This paper describes an efficient design methodology that allows starting with any kind of fuzzy controller and subsequently transforming it until a system suitable for easy DSP implementation is obtained. Such methodology is greatly aided by the design environment Xfuzzy 3. The parking problem of an autonomous robot is described to illustrate the steps of this methodology. Real experiments with the autonomous robot ROMEO 4R demonstrate efficiency of the designed fuzzy controller embedded into a stand-alone card based on a fixed-point DSP from Texas Instruments.

Complexation and Extraction of PAHs to the Aqueous Phase with a Dinuclear PtII Diazapyrenium‐Based Metallacycle

New palladium and platinum metallacycles have been synthesized by reaction between a 2,7-diazapyrenium-based ligand and Pd(II) and Pt(II) complexes. The inclusion complexes between the metallacycles and polycyclic aromatic hydrocarbons (PAHs) in CD(3)NO(2) and D(2)O were studied by NMR spectroscopy. The structures of the inclusion complexes of the Pt metallacycle as host with pyrene, phenanthrene, and triphenylene were confirmed by single crystal X-ray crystallography. The association constants between the Pt metallacycle and the selected PAHs were determined in CH(3)CN following the characteristic charge-transfer band displayed in their UV/Vis absorption spectrum. Although in aqueous solution all the complexes showed a 1:1 stoichiometry, in CH(3)CN the Job plot indicated a 2:1 stoichiometry for complexes with triphenylene and benzo[a]pyrene. The estimated association constants in water correlate with the hydrophobicity of the PAH, indicating that hydrophobic forces play an important role in the complexation process.

Self-assembly of new fluorescent Pd(II) and Pt(II) 2,7-diazapyrenium-based metallocycles and study of their inclusion complexes and [3]catenanes

New fluorescent square-shaped metallocycles were self-assembled from N-monoalkyl-2,7-diazapyrenium derivatives 1 and 4 and PdII/PtII complexes. Using ligand 1, the metal-directed self-assembly process produced a single metallocycle, while the non-symmetrical salt 4 produced mixtures of regioisomeric PdII and PtII metallocycles upon complexation with the corresponding square-planar cis-complexes. Due to the improved π-deficient character of 1 and 4 compared to related bipyridinium-based ligands, complexation and catenation of the obtained metallocycles with selected electron-rich aromatic substrates produced the corresponding 1 : 2 inclusion complexes and [3]catenanes in a highly efficient fashion. This is particularly relevant for metallocycles derived from ligand 4, as complexation and catenation occurs in a regioselective fashion, generating only the supramolecules with the appropriate parallel arrangement of the diazapyrenium subunits in order to maximize the host–guest π-stacking interactions. The potential of the new metallocycles for optical signalling applications is illustrated by analyzing their absorption and emission behaviour upon complexation and catenation.

Synthesis of platinum(II) metallocycles using microwave-assisted heating.

An efficient microwave-assisted self-assembly of dinuclear platinum metallocycles is reported. The reactions proceed to afford the products with high purity and yields within 3-4 h. We have used this methodology to synthesize a new 14.75 Å × 14.75 Å molecular square. The solid-state structure showed a perfect alignment of the squares along the c axis.

COUNTING NUMERICAL SEMIGROUPS WITH SHORT GENERATING FUNCTIONS

This paper presents a new methodology to compute the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius number) and multiplicity. First, we give theoretical results about the polynomial-time complexity of counting these semigroups. We also illustrate the methodology analyzing the cases of multiplicity 3 and 4 where some formulas for the number of numerical semigroups for any genus and Frobenius number are obtained.

DNA Binding Studies and Cytotoxicity of a Dinuclear PtII Diazapyrenium-Based Metallo-supramolecular Rectangular Box

The interaction with native DNA of a 2,7-diazapyrenium-based ligand 1 and its Pt(II) rectangular metallacycle 2 is explored through circular and linear dichroism and fluorescence spectroscopies. The metal-free ligand 1 binds through intercalation, with a binding constant of approximately 5×10(5) M(-1), whereas the metallacycle 2 binds and bends the DNA with a binding constant of 7×10(6) M(-1). PCR assays show that metallo-supramolecular box 2 interferes with DNA transactions in vitro whereas the intercalator 1 does not. The metallacycle is active against four human cancer cell lines, with IC(50) values ranging between 3.1 and 19.2 μM and shows similar levels of efficacy, but a different spectrum of activity, to cisplatin.

Partial Gröbner Bases for Multiobjective Integer Linear Optimization

This paper presents a new methodology for solving multiobjective integer linear programs (MOILP) using tools from algebraic geometry. We introduce the concept of partial Grobner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of Grobner basis for the single objective case to the case of multiple objectives, i.e., when there is a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that the partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. This property allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm “a la Buchberger” is developed to compute partial Grobner bases, and two different approaches are derived, using this methodology, for computing the entire set of Pareto-optimal solutions of any MOILP problem. Some examples illustrate the application of the algorithm, and computational experiments are reported on several families of problems.

A FULL AND FAITHFUL NERVE FOR 2-CATEGORIES

The notion of geometric nerve of a 2-category (Street, J. Pure Appl. Algebra49 (1987), 283–335) provides a full and faithful functor if regarded as defined on the category of 2-categories and lax 2-functors. Furthermore, lax 2-natural transformations between lax 2-functors give rise to homotopies between the corresponding simplicial maps. These facts allow us to prove a representation theorem of the general non-abelian cohomology of groupoids (classifying non-abelian extensions of groupoids) by means of homotopy classes of simplicial maps.

The tree of irreducible numerical semigroups with fixed Frobenius number

Abstract. In this paper we present a procedure to build the set of irreducible numerical semigroups with a fixed Frobenius number. The construction gives us a rooted tree structure for this set. Furthermore, by using the notion of Kunz-coordinates vector we translate the problem of finding such a tree into the problem of manipulating vectors with as many component as the Frobenius number.

Embedded fuzzy controllers on standard DSPs

Fuzzy controllers are used in many applications because of their rapid design by translating heuristic knowledge, robustness against perturbations, and smoothness in the control action. However, they require parallel processing and special operators (such as fuzzification or defuzzification) which are not available at standard DSPs, thus making inefficient its direct implementation. This paper describes a design methodology which allows starting with any kind of fuzzy controller and subsequently transforming it until obtaining a system suitable for DSP implementation. Such methodology is aided by Xfuzzy 3, a design environment developed by some of the authors. The parking problem of an autonomous robot is described to illustrate the steps of this methodology. Experimental results show the efficiency of the designed fuzzy controller embedded into a stand-alone card based on a fixed-point DSP from Texas Instruments.