Projeto de controladores robustos chaveados para sistemas não lineares descritos por modelos fuzzy Takagi-Sugeno

Pós-graduação em Engenharia Elétrica - FEIS

Estabilidade, desempenho e observação de estado de sistemas chaveados afins: aplicações aos conversores CC-CC

Pós-graduação em Engenharia Elétrica - FEIS

Modificação de zeros em sistemas de controle robusto utilizando LMIs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelagem e controle de sistemas fuzzy Takagi-Sugeno

Pós-graduação em Engenharia Elétrica - FEIS

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controle robusto de sistemas não lineares e chaveado de sistemas lineares usando realimentação derivativa

Pós-graduação em Engenharia Elétrica - FEIS

Flutter analysis including structural uncertainties

The common practice in industry is to perform flutter analyses considering the generalized stiffness and mass matrices obtained from finite element method (FEM) and aerodynamic generalized force matrices obtained from a panel method, as the doublet lattice method. These analyses are often reperformed if significant differences are found in structural frequencies and damping ratios determined from ground vibration tests compared to FEM. This unavoidable rework can result in a lengthy and costly process of analysis during the aircraft development. In this context, this paper presents an approach to perform flutter analysis including uncertainties in natural frequencies and damping ratios. The main goal is to assure the nominal system’s stability considering these modal parameters varying in a limited range. The aeroelastic system is written as an affine parameter model and the robust stability is verified solving a Lyapunov function through linear matrix inequalities and convex optimization

Novas condições de estabilidade de sistemas não lineares utilizando funções de Lyapunov fuzzy

Pós-graduação em Engenharia Elétrica - FEIS

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.

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.

Linear and sliding-mode control design for matrix converter-based unified power flow controllers

This paper presents the design and compares the performance of linear, decoupled and direct power controllers (DPC) for three-phase matrix converters operating as unified power flow controllers (UPFC). A simplified steady-state model of the matrix converter-based UPFC fitted with a modified Venturini high-frequency pulse width modulator is first used to design the linear controllers for the transmission line active (P) and reactive (Q) powers. In order to minimize the resulting cross coupling between P and Q power controllers, decoupled linear controllers (DLC) are synthesized using inverse dynamics linearization. DPC are then developed using sliding-mode control techniques, in order to guarantee both robustness and decoupled control. The designed P and Q power controllers are compared using simulations and experimental results. Linear controllers show acceptable steady-state behaviour but still exhibit coupling between P and Q powers in transient operation. DLC are free from cross coupling but are parameter sensitive. Results obtained by DPC show decoupled power control with zero error tracking and faster responses with no overshoot and no steady-state error. All the designed controllers were implemented using the same digital signal processing hardware.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.