Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Dynamical Analysis of Non-Repetitive Trajectories in Robotic Manipulation

A new method for the study and optimization of manu«ipulator trajectories is developed. The novel feature resides on the modeling formulation. Standard system desciptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyze. Moreover, the derived algorithms are suited to "deterministic" tasks, such as those appearing in a repetitivework, and are not well adapted to a "random" operation that occurs in intelligent systems interacting with a non-structured and changing environment. These facts motivate the development of alternative models based on distinct concepts. The proposed embedding of statistics and Fourier trasnform gives a new perspective towards the calculation and optimization of the robot trajectories in manipulating tasks.

Towards Human-like Bimanual Movements in Anthropomorphic Robots: A Nonlinear Optimization Approach

Previously we have presented a model for generating human-like arm and hand movements on an unimanual anthropomorphic robot involved in human-robot collaboration tasks. The present paper aims to extend our model in order to address the generation of human-like bimanual movement sequences which are challenged by scenarios cluttered with obstacles. Movement planning involves large scale nonlinear constrained optimization problems which are solved using the IPOPT solver. Simulation studies show that the model generates feasible and realistic hand trajectories for action sequences involving the two hands. The computational costs involved in the planning allow for real-time human robot-interaction. A qualitative analysis reveals that the movements of the robot exhibit basic characteristics of human movements.

A filter inexact-restoration method for nonlinear programming

A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669, 2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer (Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.

Maximum likelihood detection for OFDM signals with strong nonlinear distortion effects

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Linear amplification with multiple nonlinear devices

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e Computadores

Characterization of an OPCPA laser amplifier based on the nonlinear crystal YCOB

The work described in this thesis was performed at the Laboratory for Intense Lasers (L2I) of Instituto Superior Técnico, University of Lisbon (IST-UL). Its main contribution consists in the feasibility study of the broadband dispersive stages for an optical parametric chirped pulse amplifier based on the nonlinear crystal yttrium calcium oxi-borate (YCOB). In particular, the main goal of this work consisted in the characterization and implementation of the several optical devices involved in pulse expansion and compression of the amplified pulses to durations of the order of a few optical cycles (20 fs). This type of laser systems find application in fields such as medicine, telecommunications and machining, which require high energy, ultrashort (sub-100 fs) pulses. The main challenges consisted in the preliminary study of the performance of the broadband amplifier, which is essential for successfully handling pulses with bandwidths exceeding 100 nm when amplified from the μJ to 20 mJ per pulse. In general, the control, manipulation and characterization of optical phenomena on the scale of a few tens of fs and powers that can reach the PW level are extremely difficult and challenging due to the complexity of the phenomena of radiation-matter interaction and their nonlinearities, observed at this time scale and power level. For this purpose the main dispersive components were characterized in detail, specifically addressing the demonstration of pulse expansion and compression. The tested bandwidths are narrower than the final ones, in order to confirm the parameters of these elements and predict the performance for the broadband pulses. The work performed led to additional tasks such as a detailed characterization of laser oscillator seeding the laser chain and the detection and cancelling of additional sources of dispersion.

Strengthening to seismic action of reinforced columns with rectangular cross-section

The first part of this research work regards the assessment of the mathematical modelling of reinforced concrete columns confined with carbon fibre (CFRP) sheets under axial loading. The purpose was to evaluate existing analytical models, contribute to possible improvements and choose the best model(s) to be part of a new model for the prediction of the behaviour of confined columns under bending and compression. For circular columns, a wide group of authors have proposed several models specific for FRP-confined concrete. The analysis of some of the existing models was carried out by comparing these with several tested columns. Although several models predict fairly the peak load only few can properly estimate the load-strain and dilation behaviour of the columns. Square columns confined with CFRP show a more complex interpretation of their behaviour. Accordingly, the analysis of two experimental programs was carried out to propose new modelling equations for the whole behaviour of columns. The modelling results show that the analytical curves are in general agreement with the presented experimental curves for a wide range of dimensions. An analysis similar to the one done for circular columns was this turn carried out for square columns. Few models can fairly estimate the whole behaviour of the columns and with less accuracy at all levels when compared with circular columns. The second part of this study includes seven experimental tests carried out on reinforced concrete rectangular columns with rounded corners, different damage condition and with confinement and longitudinal strengthening systems. It was concluded that the use of CFRP confinement is viable and of effective performance enhancement alone and combined with other techniques, maintaining a good ductile behaviour for established threshold displacements. As regards the use of external longitudinal strengthening combined with CFRP confinement, this system is effective for the performance enhancement and viable in terms of execution. The load capacity was increased significantly, preserving also in this case a good ductile behaviour for threshold displacements. As to the numerical nonlinear modelling of the tested columns, the results show a variation of the peak load of 1% to 10% compared with tests results. The good results are partly due to the inclusion of the concrete constitutive model by Mander et al. modified by Faustino, Chastre & Paula taking into account the confinement effect. Despite the reasonable approximation to tests results, the modelling results showed higher unloading, which leads to an overestimate dissipated energy and residualdisplacement.

Analysis and design of sinusoidal quadrature RC-oscillators

Modern telecommunication equipment requires components that operate in many different frequency bands and support multiple communication standards, to cope with the growing demand for higher data rate. Also, a growing number of standards are adopting the use of spectrum efficient digital modulations, such as quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM). These modulation schemes require accurate quadrature oscillators, which makes the quadrature oscillator a key block in modern radio frequency (RF) transceivers. The wide tuning range characteristics of inductorless quadrature oscillators make them natural candidates, despite their higher phase noise, in comparison with LC-oscillators. This thesis presents a detailed study of inductorless sinusoidal quadrature oscillators. Three quadrature oscillators are investigated: the active coupling RC-oscillator, the novel capacitive coupling RCoscillator, and the two-integrator oscillator. The thesis includes a detailed analysis of the Van der Pol oscillator (VDPO). This is used as a base model oscillator for the analysis of the coupled oscillators. Hence, the three oscillators are approximated by the VDPO. From the nonlinear Van der Pol equations, the oscillators’ key parameters are obtained. It is analysed first the case without component mismatches and then the case with mismatches. The research is focused on determining the impact of the components’ mismatches on the oscillator key parameters: frequency, amplitude-, and quadrature-errors. Furthermore, the minimization of the errors by adjusting the circuit parameters is addressed. A novel quadrature RC-oscillator using capacitive coupling is proposed. The advantages of using the capacitive coupling are that it is noiseless, requires a small area, and has low power dissipation. The equations of the oscillation amplitude, frequency, quadrature-error, and amplitude mismatch are derived. The theoretical results are confirmed by simulation and by measurement of two prototypes fabricated in 130 nm standard complementary metal-oxide-semiconductor (CMOS) technology. The measurements reveal that the power increase due to the coupling is marginal, leading to a figure-of-merit of -154.8 dBc/Hz. These results are consistent with the noiseless feature of this coupling and are comparable to those of the best state-of-the-art RC-oscillators, in the GHz range, but with the lowest power consumption (about 9 mW). The results for the three oscillators show that the amplitude- and the quadrature-errors are proportional to the component mismatches and inversely proportional to the coupling strength. Thus, increasing the coupling strength decreases both the amplitude- and quadrature-errors. With proper coupling strength, a quadrature error below 1° and amplitude imbalance below 1% are obtained. Furthermore, the simulations show that increasing the coupling strength reduces the phase noise. Hence, there is no trade-off between phase noise and quadrature error. In the twointegrator oscillator study, it was found that the quadrature error can be eliminated by adjusting the transconductances to compensate the capacitance mismatch. However, to obtain outputs in perfect quadrature one must allow some amplitude error.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.

Seismic vulnerability of existing masonry buildings: Nonlinear parametric analysis

Existing masonry structures are usually associated to a high seismic vulnerability, mainly due to the properties of the materials, weak connections between floors and load-bearing walls, high mass of the masonry walls and flexibility of the floors. For these reasons, the seismic performance of existing masonry structures has received much attention in the last decades. This study presents the parametric analysis taking into account the deviations on features of the gaioleiro buildings - Portuguese building typology. The main objective of the parametric analysis is to compare the seismic performance of the structure as a function of the variations of its properties with respect to the response of a reference model. The parametric analysis was carried out for two types of structural analysis, namely for the non-linear dynamic analysis with time integration and for the pushover analysis with distribution of forces proportional to the inertial forces of the structure. The Young's modulus of the masonry walls, Young's modulus of the timber floors, the compressive and tensile non-linear properties (strength and fracture energy) were the properties considered in both type of analysis. Additionally, in the dynamic analysis, the influences of the vis-cous damping and of the vertical component of the earthquake were evaluated. A pushover analysis proportional to the modal displacement of the first mode in each direction was also carried out. The results shows that the Young's modulus of the masonry walls, the Young's modulus of the timber floors and the compressive non-linear properties are the pa-rameters that most influence the seismic performance of this type of tall and weak existing masonry structures. Furthermore, it is concluded that that the stiffness of the floors influences significantly the strength capacity and the collapse mecha-nism of the numerical model. Thus, a study on the strengthening of the floors was also carried out. The increase of the thickness of the timber floors was the strengthening technique that presented the best seismic performance, in which the reduction of the out-of-plane displacements of the masonry walls is highlighted.