Asymptotic properties of weighted least squares estimation in weak parma models

The aim of this work is to investigate the asymptotic properties of weighted least squares (WLS) estimation for causal and invertible periodic autoregressive moving average (PARMA) models with uncorrelated but dependent errors. Under mild assumptions, it is shown that the WLS estimators of PARMA models are strongly consistent and asymptotically normal. It extends Theorem 3.1 of Basawa and Lund (2001) on least squares estimation of PARMA models with independent errors. It is seen that the asymptotic covariance matrix of the WLS estimators obtained under dependent errors is generally different from that obtained with independent errors. The impact can be dramatic on the standard inference methods based on independent errors when the latter are dependent. Examples and simulation results illustrate the practical relevance of our findings. An application to financial data is also presented.Weak periodic autoregressive moving average models; Seasonality; Weighted least squares; Asymptotic normality; Strong consistency; Weak periodic white noise; Strong mixing.

Inverse modelling and inverse simulation for system engineering and control applications

Following extensive development over the past two decades, techniques of inverse simulation have led to a range of successful applications, mainly in the fields of helicopter flight mechanics, aircraft handling qualities and associated issues in terms of model validation. However, the available methods still have some well-known limitations. The traditional methods based on the Newton-Raphson algorithm suffer from numerical problems such as high-frequency oscillations and can have limitations in their applicability due to problems of input-output redundancy. The existing approaches may also show a phenomenon which has been termed “constraint oscillations” which leads to low-frequency oscillatory behaviour in the inverse solutions. Moreover, the need for derivative information may limit their applicability for situations involving manoeuvre discontinuities, model discontinuities or input constraints. Two new methods are developed to overcome these issues. The first one, based on sensitivity-analysis theory, allows the Jacobian matrix to be calculated by solving a sensitivity equation and also overcomes problems of input-output redundancy. In addition, it can improve the accuracy of results compared with conventional methods and can deal with the problem of high-frequency oscillations to some extent. The second one, based on a constrained Nelder-Mead search-based optimisation algorithm, is completely derivative-free algorithm for inverse simulation. This approach eliminates problems which make traditional inverse simulation techniques difficult to apply in control applications involving discontinuous issues such as actuator amplitude or rate limits. This thesis also offers new insight into the relationship between mathematically based techniques of model inversion and the inverse simulation approach. The similarities and shortcomings of both these methodologies are explored. The findings point to the possibility that inverse simulation can be used successfully within the control system design process for feedforward controllers for model-based output-tracking control system structures. This avoids the more complicated and relatively tedious techniques of model inversion which have been used in the past for feedforward controller design. The methods of inverse simulation presented in this thesis have been applied to a number of problems which are concerned mainly with helicopter and ship control problems and include cases involving systems having nonminimum-phase characteristics. The analysis of results for these practical applications shows that the approaches developed and presented in this thesis are of practical importance. It is believed that these developments form a useful step in moving inverse simulation methods from the status of an academic research topic to a practical and robust set of tools for engineering system design

Tight Bounds on the R\'enyi Entropy via Majorization with Applications to Guessing and Compression

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi entropy of a discrete random variable with a finite support is derived as a function of the size of the support, and the ratio of the maximal to minimal probability masses. This work was inspired by the recently published paper by Cicalese et al., which is focused on the Shannon entropy, and it strengthens and generalizes the results of that paper to R\'enyi entropies of arbitrary positive orders. In view of these generalized bounds and the works by Arikan and Campbell, non-asymptotic bounds are derived for guessing moments and lossless data compression of discrete memoryless sources.Comment: The paper was published in the Entropy journal (special issue on Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding), vol. 20, no. 12, paper no. 896, November 22, 2018. Online available at https://www.mdpi.com/1099-4300/20/12/89

The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learning

Suppose we are given access to $n$ independent samples from distribution $\mu$ and we wish to output one of them with the goal of making the output distributed as close as possible to a target distribution $\nu$. In this work we show that the optimal total variation distance as a function of $n$ is given by $\tilde\Theta(\frac{D}{f'(n)})$ over the class of all pairs $\nu,\mu$ with a bounded $f$-divergence $D_f(\nu\|\mu)\leq D$. Previously, this question was studied only for the case when the Radon-Nikodym derivative of $\nu$ with respect to $\mu$ is uniformly bounded. We then consider an application in the seemingly very different field of smoothed online learning, where we show that recent results on the minimax regret and the regret of oracle-efficient algorithms still hold even under relaxed constraints on the adversary (to have bounded $f$-divergence, as opposed to bounded Radon-Nikodym derivative). Finally, we also study efficacy of importance sampling for mean estimates uniform over a function class and compare importance sampling with rejection sampling

Asymptotic properties of weighted least squares estimation in weak parma models

The aim of this work is to investigate the asymptotic properties of weighted least squares (WLS) estimation for causal and invertible periodic autoregressive moving average (PARMA) models with uncorrelated but dependent errors. Under mild assumptions, it is shown that the WLS estimators of PARMA models are strongly consistent and asymptotically normal. It extends Theorem 3.1 of Basawa and Lund (2001) on least squares estimation of PARMA models with independent errors. It is seen that the asymptotic covariance matrix of the WLS estimators obtained under dependent errors is generally different from that obtained with independent errors. The impact can be dramatic on the standard inference methods based on independent errors when the latter are dependent. Examples and simulation results illustrate the practical relevance of our findings. An application to financial data is also presented

Contributions to cascade linear control strategies applied to grid-connected Voltage-Source Converters

El trabajo desarrollado en esta Tesis se centra en optimizar el comportamiento de Voltage-Source Converters (VSCs) cuando son utilizados como interfaz con la red eléctrica, tanto para absorber como para entregar energía de la red con la mejor calidad posible y cumpliendo con los estándares. Para tal fin, esta Tesis se centra en el control de sistemas lineales conectados en cascada aplicados al control de VSCs conectados en paralelo con la red eléctrica a través de un filtro L, especialmente en conexiones con redes débiles y en dos líneas de trabajo: (i) seguimiento de armónicos de las corrientes de red y rechazo de armónicos de las tensiones de red, y (ii) control de la tensión del PCC en caso de desequilibrio. Para ello, esta Tesis realiza contribuciones en el área del control de corriente y control de la tensión del PCC. De entre las técnicas existentes para implementar el control de corriente para compensación armónica, dos de las más utilizadas son el control resonante y el control repetitivo, tanto en ejes de referencia estacionarios como síncronos. Se ha realizado un exhaustivo estudio de diferentes estructuras para implementar tales controles, mostrando su algoritmo adaptativo en frecuencia para cada una de ellas y analizando su carga computacional. Además, se han facilitado directrices básicas para su programación en un DSP. Se ha analizado también el esquema de control de corriente para establecer una comparación entre las diferentes estructuras. Después de estudiar en profundidad el control de corriente de un VSC conectado a la red eléctrica, el segundo control a analizar es el control de tensión del PCC. La presencia de una tensión desequilibrada en el PCC da lugar a la aparición de una componente de corriente de secuencia negativa, que deteriora el comportamiento del sistema de control cuando se emplean las técnicas de control convencionales. Los STATCOMs son bien conocidos por ser una aplicación de potencia capaz de llevar a cabo la regulación de la tensión en el PCC en líneas de distribución que pueden ser susceptibles de sufrir perturbaciones. Esta Tesis propone el uso de un controlador de tensión en ejes de referencia síncronos para compensar una tensión desequilibrada a través de un STATCOM, permitiendo controlar independientemente tanto la secuencia positiva como la secuencia negativa. Además, este controlador incluye aspectos como un mecanismo de antiwindup y droop control para mejorar su comportamiento. Se han realizado varias pruebas experimentales para analizar las características de los controladores de corriente abordados en esta Tesis. Todas ellas han sido realizadas bajo las mismas condiciones de potencia, tensión y corriente, de modo que se pueden extraer resultados comparativos. Estas pruebas pretenden caracterizar la respuesta transitoria, la respuesta en régimen permanente, el comportamiento frente a saltos de frecuencia y la carga computacional de los controladores de corriente estudiados

Linear and nonlinear parametric hydrodynamic models for wave energy converters identified from recorded data

Ocean waves represent an important resource of renewable energy, which can provide a significant support to the development of more sustainable energy solutions and to the reduction ofCO2 emissions. The amount of extracted energy from the ocean waves can be increased by optimizing the geometry and the control strategy of the wave energy converter (WEC), which both require mathematical hydrodynamic models, able to correctly describe the WEC-fluid interaction. In general, the construction of a model is based on physical laws describing the system under investigation. The hydrodynamic laws are the foundation for a complete description of the WEC-fluid interaction, but their solution represents a very complex and challenging problem. Different approaches to hydrodynamic WEC-fluid interaction modelling, such as computational fluid dynamics (CFD) and linear potential theory (LPT), lead to different mathematical models, each one characterised by different accuracy and computational speed. Fully nonlinear CFD models are able to describe the full range of hydrodynamic effects, but are very computationally expensive. On the other hand, LPT is based on the strong assumptions of inviscid fluid, irrotational flow, small waves and small body motion, which completely remove the hydrodynamic nonlinearity of the WEC-fluid interaction. Linear models have good computational speed, but are not able to properly describe nonlinear hydrodynamic effects, which are relevant in some WEC power production conditions, since WECs are designed to operate over a wide range of wave amplitudes, experience large motions, and generate viscous drag and vortex shedding. The main objective of this thesis is to propose and investigate an alternative pragmatic framework, for hydrodynamic model construction, based on system identification methodologies. The goal is to obtain models which are between the CFD and LPT extremes, a good compromise able to describe the most important nonlinearities of the physical system, without requiring excessively computational time. The identified models remain sufficiently fast and simple to run in real-time. System identification techniques can ‘inject’ into the model only the information contained in the identification data; therefore, the models obtained from LPT data are not able to describe nonlinear hydrodynamic effects. In this thesis, instead of traditional LPT data, experimental wave tank data (both numerical wave tank (NWT), implemented with a CFD software package, and real wave tank (RWT)) are proposed for hydrodynamic model identification, since CFD-NWT and RWT data can contain the full range of nonlinear hydrodynamic effects. In this thesis, different typologies of wave tank experiments and excitation signals are investigated in order to generate informative data and reduce the experiment duration. Indeed, the reduction of the experiment duration represents an important advantage since, in the case of a CFD-NWT, the amount of computation time can become unsustainable whereas, in the case of a RWT, a set of long tank experiments corresponds to an increase of the facility renting costs

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI