Controle ótimo H∞ de sistemas não-lineares com modelos fuzzy takagi-sugeno

Neste trabalho é proposta uma metodologia de rastreamento de sinais e rejeição de distúrbios aplicada a sistemas não-lineares. Para o projeto do sistema de rastreamento, projeta-se os controladores fuzzy M(a) e N(a) que minimizam o limitante superior da norma H∞ entre o sinal de referência r(t) e o sinal de erro de rastreamento e(t), sendo e(t) a diferença entre a entrada de referência e a saída do sistema z(t). No método de rejeição de distúrbio utiliza-se a realimentação dinâmica da saída através de um controlador fuzzy Kc(a) que minimiza o limitante superior da norma H∞ entre o sinal de entrada exógena w(t) e o sinal de saída z(t). O procedimento de projeto proposto considera as não-linearidades da planta através dos modelos fuzzy Takagi-Sugeno. Os métodos são equacionados utilizando-se inequações matriciais lineares (LMIs), que quando factíveis, podem ser facilmente solucionados por algoritmos de convergência polinomial. Por fim, um exemplo ilustra a viabilidade da metodologia proposta.

Quasi-isometries and isoperimetric inequalities

We consider the stability of isoperimetric inequalities under quasi-isometries between Riemann surfaces. Kanai observed that quasi-isometries preserve isoperimetric inequalities on complete Riemannian manifolds with finite geometry: positive injectivity radius and Ricci curvature bounded from below (see [2]). In [1], it is shown that the linear isoperimetric inequality is a quasi-isometric invariant for planar Riemann surfaces (genus zero surfaces) with vanishing injectivity radius. Moreover, it is proved that non-linear isoperimetric inequalities can only hold for Riemann surfaces with positive injectivity radius, and hence, by Kanai's observation, preserved by quasi-isometries. In this talk we present an overview on isoperimetric inequalities and give some of the ideas of the proofs of the results cited above.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

A Monte Carlo-based procedure for independent monitor unit calculation in IMRT treatment plans.

Intensity-modulated radiotherapy (IMRT) treatment plan verification by comparison with measured data requires having access to the linear accelerator and is time consuming. In this paper, we propose a method for monitor unit (MU) calculation and plan comparison for step and shoot IMRT based on the Monte Carlo code EGSnrc/BEAMnrc. The beamlets of an IMRT treatment plan are individually simulated using Monte Carlo and converted into absorbed dose to water per MU. The dose of the whole treatment can be expressed through a linear matrix equation of the MU and dose per MU of every beamlet. Due to the positivity of the absorbed dose and MU values, this equation is solved for the MU values using a non-negative least-squares fit optimization algorithm (NNLS). The Monte Carlo plan is formed by multiplying the Monte Carlo absorbed dose to water per MU with the Monte Carlo/NNLS MU. Several treatment plan localizations calculated with a commercial treatment planning system (TPS) are compared with the proposed method for validation. The Monte Carlo/NNLS MUs are close to the ones calculated by the TPS and lead to a treatment dose distribution which is clinically equivalent to the one calculated by the TPS. This procedure can be used as an IMRT QA and further development could allow this technique to be used for other radiotherapy techniques like tomotherapy or volumetric modulated arc therapy.

Développement et validation d'une méthode de calcul indépendant des unités moniteur basée sur les simulations Monte Carlo pour la vérification des traitements IMRT

Résumé : La radiothérapie par modulation d'intensité (IMRT) est une technique de traitement qui utilise des faisceaux dont la fluence de rayonnement est modulée. L'IMRT, largement utilisée dans les pays industrialisés, permet d'atteindre une meilleure homogénéité de la dose à l'intérieur du volume cible et de réduire la dose aux organes à risque. Une méthode usuelle pour réaliser pratiquement la modulation des faisceaux est de sommer de petits faisceaux (segments) qui ont la même incidence. Cette technique est appelée IMRT step-and-shoot. Dans le contexte clinique, il est nécessaire de vérifier les plans de traitement des patients avant la première irradiation. Cette question n'est toujours pas résolue de manière satisfaisante. En effet, un calcul indépendant des unités moniteur (représentatif de la pondération des chaque segment) ne peut pas être réalisé pour les traitements IMRT step-and-shoot, car les poids des segments ne sont pas connus à priori, mais calculés au moment de la planification inverse. Par ailleurs, la vérification des plans de traitement par comparaison avec des mesures prend du temps et ne restitue pas la géométrie exacte du traitement. Dans ce travail, une méthode indépendante de calcul des plans de traitement IMRT step-and-shoot est décrite. Cette méthode est basée sur le code Monte Carlo EGSnrc/BEAMnrc, dont la modélisation de la tête de l'accélérateur linéaire a été validée dans une large gamme de situations. Les segments d'un plan de traitement IMRT sont simulés individuellement dans la géométrie exacte du traitement. Ensuite, les distributions de dose sont converties en dose absorbée dans l'eau par unité moniteur. La dose totale du traitement dans chaque élément de volume du patient (voxel) peut être exprimée comme une équation matricielle linéaire des unités moniteur et de la dose par unité moniteur de chacun des faisceaux. La résolution de cette équation est effectuée par l'inversion d'une matrice à l'aide de l'algorithme dit Non-Negative Least Square fit (NNLS). L'ensemble des voxels contenus dans le volume patient ne pouvant être utilisés dans le calcul pour des raisons de limitations informatiques, plusieurs possibilités de sélection ont été testées. Le meilleur choix consiste à utiliser les voxels contenus dans le Volume Cible de Planification (PTV). La méthode proposée dans ce travail a été testée avec huit cas cliniques représentatifs des traitements habituels de radiothérapie. Les unités moniteur obtenues conduisent à des distributions de dose globale cliniquement équivalentes à celles issues du logiciel de planification des traitements. Ainsi, cette méthode indépendante de calcul des unités moniteur pour l'IMRT step-andshootest validée pour une utilisation clinique. Par analogie, il serait possible d'envisager d'appliquer une méthode similaire pour d'autres modalités de traitement comme par exemple la tomothérapie. Abstract : Intensity Modulated RadioTherapy (IMRT) is a treatment technique that uses modulated beam fluence. IMRT is now widespread in more advanced countries, due to its improvement of dose conformation around target volume, and its ability to lower doses to organs at risk in complex clinical cases. One way to carry out beam modulation is to sum smaller beams (beamlets) with the same incidence. This technique is called step-and-shoot IMRT. In a clinical context, it is necessary to verify treatment plans before the first irradiation. IMRT Plan verification is still an issue for this technique. Independent monitor unit calculation (representative of the weight of each beamlet) can indeed not be performed for IMRT step-and-shoot, because beamlet weights are not known a priori, but calculated by inverse planning. Besides, treatment plan verification by comparison with measured data is time consuming and performed in a simple geometry, usually in a cubic water phantom with all machine angles set to zero. In this work, an independent method for monitor unit calculation for step-and-shoot IMRT is described. This method is based on the Monte Carlo code EGSnrc/BEAMnrc. The Monte Carlo model of the head of the linear accelerator is validated by comparison of simulated and measured dose distributions in a large range of situations. The beamlets of an IMRT treatment plan are calculated individually by Monte Carlo, in the exact geometry of the treatment. Then, the dose distributions of the beamlets are converted in absorbed dose to water per monitor unit. The dose of the whole treatment in each volume element (voxel) can be expressed through a linear matrix equation of the monitor units and dose per monitor unit of every beamlets. This equation is solved by a Non-Negative Least Sqvare fif algorithm (NNLS). However, not every voxels inside the patient volume can be used in order to solve this equation, because of computer limitations. Several ways of voxel selection have been tested and the best choice consists in using voxels inside the Planning Target Volume (PTV). The method presented in this work was tested with eight clinical cases, which were representative of usual radiotherapy treatments. The monitor units obtained lead to clinically equivalent global dose distributions. Thus, this independent monitor unit calculation method for step-and-shoot IMRT is validated and can therefore be used in a clinical routine. It would be possible to consider applying a similar method for other treatment modalities, such as for instance tomotherapy or volumetric modulated arc therapy.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

Mixed-signal analog-digital circuits design on the pre-diffused digital array using trapezoidal association of transistors

The mixed-signal and analog design on a pre-diffused array is a challenging task, given that the digital array is a linear matrix arrangement of minimum-length transistors. To surmount this drawback a specific discipline for designing analog circuits over such array is required. An important novel technique proposed is the use of TAT (Trapezoidal Associations of Transistors) composite transistors on the semi-custom Sea-Of-Transistors (SOT) array. The analysis and advantages of TAT arrangement are extensively analyzed and demonstrated, with simulation and measurement comparisons to equivalent single transistors. Basic analog cells were also designed as well in full-custom and TAT versions in 1.0mm and 0.5mm digital CMOS technologies. Most of the circuits were prototyped in full-custom and TAT-based on pre-diffused SOT arrays. An innovative demonstration of the TAT technique is shown with the design and implementation of a mixed-signal analog system, i. e., a fully differential 2nd order Sigma-Delta Analog-to-Digital (A/D) modulator, fabricated in both full-custom and SOT array methodologies in 0.5mm CMOS technology from MOSIS foundry. Three test-chips were designed and fabricated in 0.5mm. Two of them are IC chips containing the full-custom and SOT array versions of a 2nd-Order Sigma-Delta A/D modulator. The third IC contains a transistors-structure (TAT and single) and analog cells placed side-by-side, block components (Comparator and Folded-cascode OTA) of the Sigma-Delta modulator.

H-2 and H-infinity-optimal control for the tracking problem with zero variation

The problem of signal tracking, in the presence of a disturbance signal in the plant, is solved using a zero-variation methodology. A state feedback controller is designed in order to minimise the H-2-norm of the closed-loop system, such that the effect of the disturbance is attenuated. Then, a state estimator is designed and the modification of the zeros is used to minimise the H-infinity-norm from the reference input signal to the error signal. The error is taken to be the difference between the reference and the output signals, thereby making it a tracking problem. The design is formulated in a linear matrix inequality framework, such that the optimal solution of the stated control problem is obtained. Practical examples illustrate the effectiveness of the proposed method.

A controller design used in Lorenz synchronization chaotic system for secure communication based on LMI fuzzy control system

This paper describes a mathematical study about chaotic system and about the unified approach of chaos control via fuzzy control system based in Linear Matrix Inequality to design a controller which synchronizes the transmission/reception system. This system, that was based in Lorenz chaotic circuit, can be used for transmit signals in secure way.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

Implementation of a DC-DC converter with variable structure control of switched systems

This paper presents a control method for a class of continuous-time switched systems, using state feedback variable structure controllers. The method is applied to the control of a two-cell dc-dc buck converter and a control circuit design using the software PSpice is proposed. The design is based on Lyapunov-Metzler-SPR systems and the performance of the resulting control system is superior to that afforded by a recently-proposed alternative sliding-mode control technique. The dc-dc power converters are very used in industrial applications, for instance, in power systems of hybrid electric vehicles and aircrafts. Good results were obtained and the proposed design is also inexpensive because it uses electric components that can be easily found for the hardware implementation. Future researches on the subject include the hardware validation of the dc-dc converter controller and the robust control design of switched systems, with structural failures. © 2011 IEEE.

Design and implementation of a dc-dc converter based on variable structure control of switched systems

This paper presents a control method for a class of continuous-time switched systems, using state feedback variable structure controllers. The method is applied to the control of a non-trivial dc-dc power converter and a simple and inexpensive control circuit design, that was simulated using the software PSpice, is proposed. The design is based on Lyapunov-Metzler-SPR systems and the performance of the resulting control system is superior to that afforded by a recently proposed alternative sliding-mode control technique. © 2011 IFAC.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.