H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the H∞ fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses. A modified Takagi-Sugeno (T-S) fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. The measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses. Attention is focused on the analysis and design of H∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closed-loop T-S fuzzy control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities, which can be readily solved by using standard numerical software. Two examples are given to illustrate the effectiveness of the proposed design method

Cluster analysis of multiple planetary flow regimes

A modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them. This method was applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data. The dynamical model is governed by the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere. Clusters of point in the model's phase space are associated with either a few persistent or with many transient events. Two stationary clusters have patterns similar to unstable stationary model solutions, zonal, or blocked. Transient clusters of wave trains serve as way stations between the stationary ones. For the NH data, cluster analysis was performed in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters are found in the low-frequency band of more than 10 days, and transient clusters in the bandpass frequency window between 2.5 and 6 days. In the low-frequency band three pairs of clusters determine, respectively, EOFs 1, 2, and 3. They exhibit well-known regional features, such as blocking, the Pacific/North American (PNA) pattern and wave trains. Both model and low-pass data show strong bimodality. Clusters in the bandpass window show wave-train patterns in the two jet exit regions. They are related, as in the model, to transitions between stationary clusters

Stabilizing Fuzzy Control via Output Feedback

The chapter presents new conditions suitable in design of stabilizing static as well as dynamic output controllers for a class of continuous-time nonlinear systems represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure, and applying the fuzzy control scheme relating to the parallel-distributed output compensators, the sufficient design conditions are outlined in the terms of linear matrix inequalities. Depending on the proposed procedures, the Lyapunov matrix can be decoupled from the system parameter matrices using linear matrix inequality techniques or a fuzzy-relaxed approach can be applied to make closed-loop dynamics faster. Numerical examples illustrate the design procedures and demonstrate the performances of the proposed design methods

Domain walls between gauge theories

Noncommutative U(N) gauge theories at different N may be often thought of as different sectors of a single theory: the U(1) theory possesses a sequence of vacua labeled by an integer parameter N, and the theory in the vicinity of the N-th vacuum coincides with the U(N) noncommutative gauge theory. We construct noncommutative domain walls on fuzzy cylinder, separating vacua with different gauge theories. These domain walls are solutions of BPS equations in gauge theory with an extra term stabilizing the radius of the cylinder. We study properties of the domain walls using adjoint scalar and fundamental fermion fields as probes. We show that the regions on different sides of the wall are not disjoint even in the low energy regime -- there are modes penetrating from one region to the other. We find that the wall supports a chiral fermion zero mode. Also, we study non-BPS solution representing a wall and an antiwall, and show that this solution is unstable. We suggest that the domain walls emerge as solutions of matrix model in large class of pp-wave backgrounds with inhomogeneous field strength. In the M-theory language, the domain walls have an interpretation of a stack of branes of fingerstall shape inserted into a stack of cylindrical branes.Comment: Final version; minor corrections; to appear in Nucl.Phys.

Robust stabilization and observation of positive Takagi-Sugeno systems

Esta tesis propone metodologías para diseñar controladores robustos y observadores para los sistemas positivos descritos por modelos de Takagi-Sugeno (TS), lineal, inciertos, y tal vez con retraso. Las condiciones de síntesis se expresan como LMIs (desigualdades matriciales lineales). En la primera parte, se establecen las condiciones para garantizar la estabilización asintótica y la α-estabilización de los sistemas T-S lineales positivas y, tal vez afectados por incertidumbres de intervalo, usando controladores de retroalimentación de estado descompuestos. En la segunda parte, se dan las condiciones necesarias y suficientes para la estabilización de los sistemas de T-S positivos con retraso, en dos casos: cuando las variables de premisa del sistema son medibles o no. Además, el problema de diseño de control basado en observador es considerado, por las leyes de retroalimentación del estado que se pueden elegir con o sin memoria. Para mostrar la eficacia de los métodos propuestos, se proporcionan ejemplos numéricos y prácticos, dando resultados satisfactorios.Departamento de Ingeniería de Sistemas y Proceso