On the multi‐input second‐order sliding mode control of nonlinear uncertain systems

This note addresses the multi‐input second‐order sliding mode control design for a class of nonlinear multivariable uncertain dynamics. Among the most important peculiarities of the considered control problem, the considered sliding vector variable has a uniform vector relative degree [2,2, … ,2] with respect to the vector control variable, and only the sign of the sliding vector and of its derivative are available for feedback. Additionally, the symmetric part of the state‐dependent control matrix is supposed to be positive definite. Under some further mild restrictions on the uncertain system's dynamics, a control algorithm that realizes a multi‐input version of the ‘twisting’ second‐order sliding mode control algorithm is suggested. Simple controller tuning conditions are derived by means of a constructive Lyapunov analysis, which demonstrates that the suggested control algorithm guarantees the semiglobal asymptotic convergence to the sliding manifold. Simulation results, which confirm the good performance of the proposed scheme and investigate the actual accuracy obtained under the discrete‐time implementation effects, are given. Copyright © 2011 John Wiley & Sons, Ltd.     

Fast support vector machines for convolution tree kernels

Feature engineering is one of the most complex aspects of system design in machine learning. Fortunately, kernel methods provide the designer with formidable tools to tackle such complexity. Among others, tree kernels (TKs) have been successfully applied for representing structured data in diverse domains, ranging from bioinformatics and data mining to natural language processing. One drawback of such methods is that learning with them typically requires a large number of kernel computations (quadratic in the number of training examples) between training examples. However, in practice substructures often repeat in the data which makes it possible to avoid a large number of redundant kernel evaluations. In this paper, we propose the use of Directed Acyclic Graphs (DAGs) to compactly represent trees in the training algorithm of Support Vector Machines. In particular, we use DAGs for each iteration of the cutting plane algorithm (CPA) to encode the model composed by a set of trees. This enables DAG kernels to efficiently evaluate TKs between the current model and a given training tree. Consequently, the amount of total computation is reduced by avoiding redundant evaluations over shared substructures. We provide theory and algorithms to formally characterize the above idea, which we tested on several datasets. The empirical results confirm the benefits of the approach in terms of significant speedups over previous state-of-the-art methods. In addition, we propose an alternative sampling strategy within the CPA to address the class-imbalance problem, which coupled with fast learning methods provides a viable TK learning framework for a large class of real-world applications.     

Characterisation of mortar morphology in thin sections by digital image processing

A digital imaging approach was applied to investigate mortar morphology in thin sections; in particular, the binder/aggregate ratio and the grading curve of five mortar bars were attained by digital image processing (DIP), using the Image Pro Plus 4.1 software package. The imaging procedure employed image segmentation, to extract mortar aggregate, and image filtering, to fix grain boundaries. The results show that digital image processing may be considered as an alternative method to mechanical sieving for the characterisation of mortar morphology, as it appears to be quicker and more accurate than the traditional method. However, digital image processing exhibits limits, which are discussed in the text.     

Selective Complexation and Membrane Transport of Guanidinium Salts by Calix[6]arene Amides

The p-tert-butylcalix[6]arene hexamide 2 and syn-1,3,5–trimethoxy-2,4,6-triamide 4 were synthesized by reaction of α-chloro-N,N-diethylacetamide and the corresponding calix[6]arenes 1 and 3 , respectively. ¹H NMR spectroscopy shows that 2 is a mixture of different conformations whereas 4 is fixed in a cone conformation. Extraction experiments, (S-L) and (H₂O–CDCl₃) with picrate salts, indicate that 2 complexes both alkali metal (1:2 complex) and guanidinium salts (1:1 complex) but 4 complexes only guanidinium (1:1 complex). Incorporated in supported liquid membranes (Accurel^® / o-nitrophenyl n-octyl ether) the calixarenes 2 and 4 transport guanidinium salts. The hexamide 2 is a more efficient carrier of guanidinium but the syn-1,3,5-trimethoxy-2,4,6-triamide 4 is much more selective. Both 2 and 4 are sufficiently lipophilic to give membranes that are stable over longer periods (weeks).     

Recycled poly(ethylene terephthalate) and its short glass fibres composites: effects of hygrothermal aging on the thermo-mechanical behaviour

This paper reports on the effects of hygrothermal aging at 70 °C in water and at 80% relative humidity, on the thermo-mechanical properties, molar mass and microstructure of recycled poly(ethylene terephthalate) (rPET) and its short glass fibres composites.For all the investigated materials, the elastic mechanical properties (tensile and storage moduli) determined at low strain levels resulted practically unaffected by hygrothermal aging under the selected conditions. On the other hand, a marked reduction of the tensile strength and apparent fracture toughness has been observed for rPET matrix and its composites during hygrothermal aging, more markedly for materials immersed in water than for those aged at 80% RH. Both properties resulted to be related on the molar mass of the rPET matrix, that decreased during hygrothermal aging as a consequence of the hydrolysis process.The materials glass transition, evaluated as the temperature of the loss factor peak, increased during hygrothermal aging due to the progressively restricted mobility of the amorphous phase caused by a concurrent crystallinity increase. This crystallization process (chemicrystallization) is favoured by temperature, by the plasticizing effect of water and by the reduction of molar mass.Consistently with the mechanical measurements, the morphology of fracture surfaces exposed to hygrothermal aging in water revealed a reduction of plastic deformation of the rPET matrix and a weakening of the fibre-matrix interface for rPET composites.     

EXPERIMENTAL STUDIES OF NUCLEATION PHENOMENA WITHIN THERMAL BOUNDARY LAYERS—INFLUENCE ON CHEMICAL VAPOR DEPOSITION RATE PROCESSES

In carrying out partial vapor condensations using actively cooled surfaces it is known that 'mist' formation can occur within thermal boundary layers (Rosner and Epstein, 1968), dramatically modifying total deposition fluxes. Using a combination of flash-evaporation (Rosner and Liang, 1986) and laser probing techniques, we report new experimental results on binary alkali salt (K₂SO₄ + Na₂SO₄) deposition from combustion gases showing that the deposition rate of potassium sulfate first increases with the addition of sodium sulfate until the concentration of Na₂SO₄ reaches a (target surface temperature dependent) 'threshold' value. Further increases in the concentration of Na₂SO₄ dramatically decrease the total deposition rate of K₂SO₄, implying that potassium sulfate-containing microdroplets are formed within the thermal boundary layer, which, despite their thermophoretic drift toward the target, are not collected as effectively as the 'parent' K₂SO₄-vapor species. Laser light scattering measurements clearly reveal that suspended particles exist near the deposition surface under these conditions. Our experimental results on mass transfer rate and light scattering are consistent with those predicted using laminar boundary layer theory (Castillo and Rosner, 1989b) coupling both binary salt vapor deposition with particle vapor scavenging and deposition. Comparisons of our observed mist onset conditions (implying critical supersaturations near unity) with those expected using homogeneous nucleation theory suggest that the binary alkali sulfate mist nucleation mechanism is, instead, heterogeneous, even in our relatively 'clean' combustion products. Because of the; well-known vapor pressure reduction phenomenon associated here with the formation of non-ideal solutions, binary systems are shown to provide convenient 'vehicles' to investigate BL mist formation onset conditions and CVD-rate consequences without requiring the more extreme surface coolings characteristic of unary condensible vapor systems. An understanding of this dramatic phenomenon, obtained via such laboratory experiments and calculations, will allow its inclusion in future deposition rate calculations of engineering importance.     

What Borromini Might Have Known About Ovals. Ruler and Compass Constructions

This paper is about drawing ovals using a given number of certain parameters. New constructions are displayed, including the case when the symmetry axes are not given. Many of these constructions make use of a recent conjecture by Ragazzo, for which a Euclidean proof is found, thus suggesting it might have been known at the time Borromini chose the ovals for the dome of San Carlo alle Quattro Fontane. A geometric proof of the same conjecture—as well as constructions—in the more general case of eggs and polycentric curves is the subject of the first part of this same research (Mazzotti, a Euclidean approach to eggs and polycentric curves, 2014).     

Stationary policies for lower bounds on the minimum average cost of discrete‐time nonlinear control systems

The paper deals with the control problem of discrete‐time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long‐run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state‐feedback control problem, and the derived strategy is used to design a real‐time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state‐feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright © 2013 John Wiley & Sons, Ltd.