Pre-Schauder Bases in Topological Vector Spaces

A Schauder basis in a real or complex Banach space X is a sequence (en)n is an element of N in X such that for every x is an element of X there exists a unique sequence of scalars (lambda n)n is an element of N satisfying that x= n-ary sumation n=1 infinity lambda nen. Schauder bases were first introduced in the setting of real or complex Banach spaces but they have been transported to the scope of real or complex Hausdorff locally convex topological vector spaces. In this manuscript, we extend them to the setting of topological vector spaces over an absolutely valued division ring by redefining them as pre-Schauder bases. We first prove that, if a topological vector space admits a pre-Schauder basis, then the linear span of the basis is Hausdorff and the series linear span of the basis minus the linear span contains the intersection of all neighborhoods of 0. As a consequence, we conclude that the coefficient functionals are continuous if and only if the canonical projections are also continuous (this is a trivial fact in normed spaces but not in topological vector spaces). We also prove that, if a Hausdorff topological vector space admits a pre-Schauder basis and is w*-strongly torsionless, then the biorthogonal system formed by the basis and its coefficient functionals is total. Finally, we focus on Schauder bases on Banach spaces proving that every Banach space with a normalized Schauder basis admits an equivalent norm closer to the original norm than the typical bimonotone renorming and that still makes the basis binormalized and monotone. We also construct an increasing family of left-comparable norms making the normalized Schauder basis binormalized and show that the limit of this family is a right-comparable norm that also makes the normalized Schauder basis binormalized

Static compensation on the basis of NNBM predictor under Foundation Fieldbus

World Automation Congress, WAC 2004, Sevilla, SpainThis paper deals with the problem of disturbance compensation by means of a novel feedforward control procedure. It consists in the additive association of a conventional feedback control action with the prediction of the steady state control effort necessary to keep the controlled plant under setpoint requirements. Such steady state control effort is achieved by means of inverse neural network based modelling prediction. Predictors are based in an inverse neural network steady state plant model. Implementation procedure is carried out with the facilities supplied by a FOUNDATION Fieldbus compliant tool which manage databases, neural network structures and training algorithmsMinisterio de Ciencia y Tecnología; DPI2003-0051

A complement to autotuning methods on PID controllers

[Abstract] This paper describes a complement to the autotuning ATV method. The proposed strategy is based in a frequency response design technique to get a three-term controller as a special case of a lead-lag design. The main topic of such autotuning technique concerns to the type of excitation signal on the plant which is a sine wave openloop excitation instead of a relay feedback used in the harmonic balanc

Supervisión de la simulación de procesos de control mediante ecuaciones de paridad FF

[Resumen] Este artículo describe la tarea de supervisión del proceso de simulación en tiempo real de procesos de control. El algoritmo propuesto de supervisión del proceso de simulación está basado en el procesamiento masivamente paralelo de ecuaciones de paridad, en donde se comparan datos actuales reales con la salida dinámica del modelo de proceso. Si los residuos de las ecuaciones de paridad están dentro de límites admisibles entonces la información de inicialización y actualización del modelo de simulación, es admitida y el proceso de simulación es validad

Multivariable fuzzy cascade compensation

This work deals with some practical aspects of fuzzy PID controllers regarding multivariable non-linear cascade compensation. This contribution concerns to the task of compensation for multivariable disturbances on the manipulated variable. The strategy consists in establishing a fuzzy rule base for all disturbance variables which afect the manipulated variable and compensate the control variable by cascade action by means of the proposed fuzzy rule base properly adjuste

Spanish public finances through the financial crisis

El desempeño de la actividad de las Administraciones Públicas ha estado sometido a un elevado grado de tensión durante la crisis soberana reciente, a pesar del reducido nivel de deuda pública y de los superávits presupuestarios registrados en el período inmediatamente anterior a la crisis. El impacto de la recesión y una fase inicial de actuación contracíclica de la política fiscal exacerbaron las vulnerabilidades estructurales latentes de las finanzas públicas. El proceso de corrección de estos desequilibrios presupuestarios ha requerido la puesta en marcha de un conjunto de medias en los ámbitos de la imposición, el gasto público, el marco de reglas fiscales nacionales y la estructura del sector público. En este contexto, el presente documento discute la evolución de las finanzas públicas durante la crisis, prestando especial atención a las políticas de respuesta a la crisis financiera y a las tendencias macroeconómicas de medio plazo en las que se insertanSpain’s public finances have been under signifi cant stress during the crisis, despite precrisis fiscal surpluses and low levels of public debt. The impact of the crisis and an initial phase of counter-cyclical activism exacerbated the existing (structural) fiscal vulnerabilities. To correct the fiscal imbalances, a significant number of bold policy actions were taken, affecting taxation, public spending, national fi scal rules and the structure of the public sector. In this paper we discuss the evolution of public finances in Spain during the financial crisis, framing crisis-related fiscal policy measures within medium-term economic trends and focusing on policy responses to the financial crisis. We also touch upon the main policy challenges ahea

Hybrid modelling using neural network based prediction under Foundation Fieldbus

World Automation Congress, WAC 2004, Sevilla, SpainThe objective of this work is to describe a novel methodology for modelling MV and NL processes, useful among other applications, in fault detection tasks, possibly to be applied on plant supervision, including transient state fault detection and decision making according the well known method based on parity equations and rule based residuals evaluationMinisterio de Ciencia y Tecnología; DPI2003-0051