Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Control of uncertain compartmental systems

Os sistemas compartimentais são frequentemente usados na modelação de diversos processos em várias áreas, tais como a biomedicina, ecologia, farmacocinética, entre outras. Na maioria das aplicações práticas, nomeadamente, aquelas que dizem respeito à administração de drogas a pacientes sujeitos a cirurgia, por exemplo, a presença de incertezas nos parâmetros do sistema ou no estado do sistema é muito comum. Ao longo dos últimos anos, a análise de sistemas compartimentais tem sido bastante desenvolvida na literatura. No entanto, a análise da sensibilidade da estabilidade destes sistemas na presença de incertezas tem recebido muito menos atenção. Nesta tese, consideramos uma lei de controlo por realimentação do estado com restrições de positividade e analisamos a sua robustez quando aplicada a sistemas compartimentais lineares e invariantes no tempo com incertezas nos parâmetros. Além disso, para sistemas lineares e invariantes no tempo com estado inicial desconhecido, combinamos esta lei de controlo com um observador do estado e a robustez da lei de controlo resultante também é analisada. O controlo do bloqueio neuromuscular por meio da infusão contínua de um relaxante muscular pode ser modelado como um sistema compartimental de três compartimentos e tem sido objecto de estudo por diversos grupos de investigação. Nesta tese, os nossos resultados são aplicados a este problema de controlo e são fornecidas estratégias para melhorar os resultados obtidos.

Fractional control of heat diffusion systems

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

Numerical modelling of two-way propagation of non-linear dispersive waves

We describe and implement a fully discrete spectral method for the numerical solution of a class of non-linear, dispersive systems of Boussinesq type, modelling two-way propagation of long water waves of small amplitude in a channel. For three particular systems, we investigate properties of the numerically computed solutions; in particular we study the generation and interaction of approximate solitary waves.

A comparison of test of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We evaluate the forecasting performance of a number of systems models of US shortand long-term interest rates. Non-linearities, induding asymmetries in the adjustment to equilibrium, are shown to result in more accurate short horizon forecasts. We find that both long and short rates respond to disequilibria in the spread in certain circumstances, which would not be evident from linear representations or from single-equation analyses of the short-term interest rate.

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Less Conservative Control Design for Linear Systems with Polytopic Uncertainties via State-Derivative Feedback

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

CONTROL OF UNCERTAIN DYNAMIC-SYSTEMS USING STRICTLY POSITIVE REAL SYSTEMS

This paper presents necessary and sufficient conditions to turn a linear time-invariant system with p outputs, m inputs, p greater-than-or-equal-to m and using only inputs and outputs measurements into a Strictly Positive Real (SPR).Two results are presented. In the first, the system compensation is made by two static compensators, one of which forward feeds the outputs and the second back feeds the outputs of the nominal system.The second result presents conditions for the Walcott and Zak variable structure observer-controller synthesis. In this problem, if the nominal system is given by {A,B,C}, then the compensated system is given by {A+GC,B,FC} where F and G are the constant compensation matrices. These results are useful in the control system with uncertainties.

Stochastic exponential stability of singular linear systems with Markov jump parameters

This paper deals with exponential stability of discrete-time singular systems with Markov jump parameters. We propose a set of coupled generalized Lyapunov equations (CGLE) that provides sufficient conditions to check this property for this class of systems. A method for solving the obtained CGLE is also presented, based on iterations of standard singular Lyapunov equations. We present also a numerical example to illustrate the effectiveness of the approach we are proposing.

A new method for continuous quality control of nsm cfrp systems

In the last decade the near-surface mounted (NSM) strengthening technique using carbon fibre reinforced polymers (CFRP) has been increasingly used to improve the load carrying capacity of concrete members. Compared to externally bonded reinforcement (EBR), the NSM system presents considerable advantages. This technique consists in the insertion of carbon fibre reinforced polymer laminate strips into pre-cut slits opened in the concrete cover of the elements to be strengthened. CFRP reinforcement is bonded to concrete with an appropriate groove filler, typically epoxy adhesive or cement grout. Up to now, research efforts have been mainly focused on several structural aspects, such as: bond behaviour, flexural and/or shear strengthening effectiveness, and energy dissipation capacity of beam-column joints. In such research works, as well as in field applications, the most widespread adhesives that are used to bond reinforcements to concrete are epoxy resins. It is largely accepted that the performance of the whole application of NSM systems strongly depends on the mechanical properties of the epoxy resins, for which proper curing conditions must be assured. Therefore, the existence of non-destructive methods that allow monitoring the curing process of epoxy resins in the NSM CFRP system is desirable, in view of obtaining continuous information that can provide indication in regard to the effectiveness of curing and the expectable bond behaviour of CFRP/adhesive/concrete systems. The experimental research was developed at the Laboratory of the Structural Division of the Civil Engineering Department of the University of Minho in Guimar\~aes, Portugal (LEST). The main objective was to develop and propose a new method for continuous quality control of the curing of epoxy resins applied in NSM CFRP strengthening systems. This objective is pursued through the adaptation of an existing technique, termed EMM-ARM (Elasticity Modulus Monitoring through Ambient Response Method) that has been developed for monitoring the early stiffness evolution of cement-based materials. The experimental program was composed of two parts: (i) direct pull-out tests on concrete specimens strengthened with NSM CFRP laminate strips were conducted to assess the evolution of bond behaviour between CFRP and concrete since early ages; and, (ii) EMM-ARM tests were carried out for monitoring the progressive stiffness development of the structural adhesive used in CFRP applications. In order to verify the capability of the proposed method for evaluating the elastic modulus of the epoxy, static E-Modulus was determined through tension tests. The results of the two series of tests were then combined and compared to evaluate the possibility of implementation of a new method for the continuous monitoring and quality control of NSM CFRP applications.

X-parameters based analytical design of non-linear microwave circuits Application to oscillator design

Resumen El diseño clásico de circuitos de microondas se basa fundamentalmente en el uso de los parámetros s, debido a su capacidad para caracterizar de forma exitosa el comportamiento de cualquier circuito lineal. La relación existente entre los parámetros s con los sistemas de medida actuales y con las herramientas de simulación lineal han facilitado su éxito y su uso extensivo tanto en el diseño como en la caracterización de circuitos y subsistemas de microondas. Sin embargo, a pesar de la gran aceptación de los parámetros s en la comunidad de microondas, el principal inconveniente de esta formulación reside en su limitación para predecir el comportamiento de sistemas no lineales reales. En la actualidad, uno de los principales retos de los diseñadores de microondas es el desarrollo de un contexto análogo que permita integrar tanto el modelado no lineal, como los sistemas de medidas de gran señal y los entornos de simulación no lineal, con el objetivo de extender las capacidades de los parámetros s a regímenes de operación en gran señal y por tanto, obtener una infraestructura que permita tanto la caracterización como el diseño de circuitos no lineales de forma fiable y eficiente. De acuerdo a esta filosofía, en los últimos años se han desarrollado diferentes propuestas como los parámetros X, de Agilent Technologies, o el modelo de Cardiff que tratan de proporcionar esta plataforma común en el ámbito de gran señal. Dentro de este contexto, uno de los objetivos de la presente Tesis es el análisis de la viabilidad del uso de los parámetros X en el diseño y simulación de osciladores para transceptores de microondas. Otro aspecto relevante en el análisis y diseño de circuitos lineales de microondas es la disposición de métodos analíticos sencillos, basados en los parámetros s del transistor, que permitan la obtención directa y rápida de las impedancias de carga y fuente necesarias para cumplir las especificaciones de diseño requeridas en cuanto a ganancia, potencia de salida, eficiencia o adaptación de entrada y salida, así como la determinación analítica de parámetros de diseño clave como el factor de estabilidad o los contornos de ganancia de potencia. Por lo tanto, el desarrollo de una formulación de diseño analítico, basada en los parámetros X y similar a la existente en pequeña señal, permitiría su uso en aplicaciones no lineales y supone un nuevo reto que se va a afrontar en este trabajo. Por tanto, el principal objetivo de la presente Tesis consistiría en la elaboración de una metodología analítica basada en el uso de los parámetros X para el diseño de circuitos no lineales que jugaría un papel similar al que juegan los parámetros s en el diseño de circuitos lineales de microondas. Dichos métodos de diseño analíticos permitirían una mejora significativa en los actuales procedimientos de diseño disponibles en gran señal, así como una reducción considerable en el tiempo de diseño, lo que permitiría la obtención de técnicas mucho más eficientes. Abstract In linear world, classical microwave circuit design relies on the s-parameters due to its capability to successfully characterize the behavior of any linear circuit. Thus the direct use of s-parameters in measurement systems and in linear simulation analysis tools, has facilitated its extensive use and success in the design and characterization of microwave circuits and subsystems. Nevertheless, despite the great success of s-parameters in the microwave community, the main drawback of this formulation is its limitation in the behavior prediction of real non-linear systems. Nowadays, the challenge of microwave designers is the development of an analogue framework that allows to integrate non-linear modeling, large-signal measurement hardware and non-linear simulation environment in order to extend s-parameters capabilities to non-linear regimen and thus, provide the infrastructure for non-linear design and test in a reliable and efficient way. Recently, different attempts with the aim to provide this common platform have been introduced, as the Cardiff approach and the Agilent X-parameters. Hence, this Thesis aims to demonstrate the X-parameter capability to provide this non-linear design and test framework in CAD-based oscillator context. Furthermore, the classical analysis and design of linear microwave transistorbased circuits is based on the development of simple analytical approaches, involving the transistor s-parameters, that are able to quickly provide an analytical solution for the input/output transistor loading conditions as well as analytically determine fundamental parameters as the stability factor, the power gain contours or the input/ output match. Hence, the development of similar analytical design tools that are able to extend s-parameters capabilities in small-signal design to non-linear ap- v plications means a new challenge that is going to be faced in the present work. Therefore, the development of an analytical design framework, based on loadindependent X-parameters, constitutes the core of this Thesis. These analytical nonlinear design approaches would enable to significantly improve current large-signal design processes as well as dramatically decrease the required design time and thus, obtain more efficient approaches.

Real-time load-side control of electric power systems

Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.

(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control.

(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.