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

Contributions to nonlinear system modelling and controller synthesis via convex structures

Esta tesis discute diferentes metodologías de modelado para extraer mejores prestaciones o resultados de estabilidad que aquéllas que el modelado convencional basado en sector no-lineal de sistemas Takagi-Sugeno (también denominados cuasi-LPV) es capaz de producir. En efecto, incluso si las LMIs pueden probar distintas cotas de prestaciones o márgenes de estabilidad (tasa de decaimiento, $\mathcal H_\infty$, etc.) para sistemas politópicos, es bien conocido que las prestaciones probadas dependen del modelo elegido y, dado un sistema no-lineal, dicho modelo politópico no es único. Por tanto, se presentan exploraciones hacia cómo obtener el modelo que es menos perjudicial para la medida de prestaciones elegida. Como una última contribución, mejores resultados son obtenidos mediante la extensión del modelado politópico Takagi-Sugeno a un marco de inclusiones en diferencias cuasi-convexas con planificación de ganancia. En efecto, una versión sin planificación de ganancia fue propuesta por un equipo de investigadores de la Universidad de Sevilla (Fiaccini, Álamo, Camacho) para generalizar el modelado politópico, y esta tesis propone una version aún más general de algunos de dichos resultados que incorpora planificación de ganancia.This thesis discusses different modelling methodologies to eke out best performance/stability results than conventional sector-nonlinearity Takagi-Sugeno (also known as quasi-LPV) systems modelling techniques are able to yield. Indeed, even if LMIs can prove various performance and stability bounds (decay rate, $\mathcal H_\infty$, etc.) for polytopic systems, it is well known that the proven performance depends on the chosen model and, given a nonlinear dynamic systems, the polytopic embeddings available for it are not unique. Thus, explorations on how to obtain the model which is less deletereous for performance are presented. As a last contribution, extending the polytopic Takagi-Sugeno setup to a gain-scheduled quasi-convex difference inclusion framework allows to improve the results over the polytopic models. Indeed, the non-scheduled convex difference inclusion framework was proposed by a research team in University of Seville (Fiacchini, Alamo, Camacho) as a generalised modelling methodology which included the polytopic one; this thesis poses a further generalised gain-scheduled version of some of these results.Aquesta tesi discuteix diferents metodologies de modelatge per extreure millors prestacions o resultats d'estabilitat que aquelles que el modelatge convencional basat en sector no-lineal de sistemes Takagi-Sugeno (també anomenats quasi-LPV) és capaç de produir. En efecte, fins i tot si les LMIs poden provar diferents cotes de prestacions o marges d'estabilitat (taxa de decaïment, $\mathcal H_\infty$, etc.) per a sistemes politòpics, és ben conegut que les prestacions provades depenen del model triat i, donat un sistema no-lineal, el dit model politòpic no és únic. Per tant, es presenten exploracions cap a com obtenir el model que és menys perjudicial per a la mesura de prestacions triada. Com una darrera contribució, millors resultats són obtinguts mitjançant l'extensió del modelatge politòpic Takagi-Sugeno a un marc d'inclusions en diferències quasi-convexes amb planificació de guany. En efecte, una versió sense planificació de guany va ser proposada per un equip d'investigadors de la Universitat de Sevilla (Fiaccini, Álamo, Camacho) per a generalitzar el modelatge politòpic, i aquesta tesi proposa una versió més general d'alguns d'aquests resultats que incorpora planificació de guany.Robles Ruiz, R. (2018). Contributions to nonlinear system modelling and controller synthesis via convex structures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/100848TESI

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

TS fuzzy approach for modeling, analysis and design of non-smooth dynamical systems

There has been growing interest in the past two decades in studying the physical model of dynamical systems that can be described by nonlinear, non-smooth differential equations, i.e. non-smooth dynamical systems. These systems exhibit more colourful and complex dynamics compared to their smooth counterparts; however, their qualitative analysis and design are not yet fully developed and still open to exploration. At the same time, Takagi-Sugeno (TS) fuzzy systems have been shown to have a great ability to represent a large class of nonlinear systems and approximate their inherent uncertainties. This thesis explores an area of TS fuzzy systems that have not been considered before; that is, modelling, stability analysis and design for non-smooth dynamical systems. TS fuzzy model structures capable of representing or approximating the essential dis- continuous dynamics of non-smooth systems are proposed in this thesis. It is shown that by incorporating discrete event systems, the proposed structure for TS fuzzy models, which we will call non-smooth TS fuzzy models, can accurately represent the smooth (or contin- uous) as well as non-smooth (or discontinuous) dynamics of different classes of electrical and mechanical non-smooth systems including (sliding and non-sliding) Filippov's systems and impacting systems. The different properties of the TS fuzzy modelling (or formalism) are discussed. It is highlighted that the TS fuzzy formalism, taking advantage of its simple structure, does not need a special platform for its implementation. Stability in its new notion of structural stability (stability of a periodic solution) is one of the most important issues in the qualitative analysis of non-smooth systems. An important part of this thesis is focused on addressing stability issues by extending non- smooth Lyapunov theory for verifying the stability of local orbits, which the non-smooth TS fuzzy models can contain. Stability conditions are proposed for Filippov-type and impacting systems and it is shown that by formulating the conditions as Linear Matrix inequalities (LMIs), the onset of non-smooth bifurcations or chaotic phenomena can be detected by solving a feasibility problem. A number of examples are given to validate the proposed approach. Stability robustness of non-smooth TS fuzzy systems in the presence of model uncertainties is discussed in terms of non-smoothness rather than traditional observer design. The LMI stabilization problem is employed as a building block for devising design strategies to suppress the unwanted chaotic behaviour in non-smooth TS fuzzy models. There have been a large number of control applications in which the overall closed-loop sys tem can be stabilized by switching between pre-designed sub-controllers. Inspired by this idea, the design part of this thesis concentrates on fuzzy-chaos control strategies for Filippov-type systems. These strategies approach the design problem by switching be- tween local state-feedback controllers such that the closed-loop TS fuzzy system of interest rapidly converges to the stable periodic solution of the system. All control strategies are also automated as a design problem recast on linear matrix inequality conditions to be solved by modern optimization techniques. Keywords: Takagi-Sugeno fuzzy systems, non-smooth Lyapunov theory, non-smooth dy- namical systems, piecewise-smooth dynamical systems, structural stability, discontinuity- induced bifurcation, chaos controllers, dc-dc converters, Filippov's system, impacting system, linear matrix inequalities.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Event-triggered synchronization of saturated lur’e type systems

This dissertation addresses the problem of master-slave synchronization of nonlinear discrete-time Lur’e systems subject to input saturation via event-triggered control (ETC) techniques. Synchronization, which is considered a remarkable property in the physics literature specially when chaotic systems are under investigation, is achieved through the stabilization of the error between the states of the master and the slave system. Regarding the Lur’e type nonlinearity, two different cases are studied along this work: generic slope-restricted state-dependent nonlinearity and piecewise-affine function. In the ETC paradigm, the control signal is updated aperiodically only after the occurrence of an event, which is generated according to a triggering criterion that depends on the evaluation of a triggering function. In the emulation-based design, a synchronization error feedback controller is given a priori and the task is to compute the event generator parameters ensuring performance and closed-loop stability. On the other hand, in the co-design approach the event generator and the control law are simultaneously designed. Theoretical results are obtained for three types of event-triggered mechanism (ETM), namely: static, dynamic and relaxed. In the last case, practical synchronization conditions are derived as form of ultimately boundedness stability. In order to tune the parameters of the event-based strategy, optimization problems are formulated aiming to reduce the number of control signal updates (number of events) with respect to a time-triggered implementation. Numerical simulations are presented to illustrate the application of the proposed methods.Esta dissertação aborda o problema de sincronização mestre-escravo de sistemas Lur’e não lineares de tempo discreto sujeitos à saturação de entrada via técnicas de controle baseado em eventos. A sincronização, que é considerada uma propriedade importante na literatura de Física especialmente quando sistemas caóticos são investigados, é alcançada através da estabilização do erro entre os estados do mestre e do sistema escravo. Em relação à não linearidade do tipo Lur’e, dois casos diferentes são estudados ao longo do trabalho: não linearidade genérica dependente do estado e restrita em inclinação e função afim por partes. No paradigma de controle baseado em eventos (ETC), o sinal de controle é atualizado aperiodicamente apenas após a ocorrência de um evento, que é gerado de acordo com um critério de disparo que depende da avaliação de uma função de disparo. No projeto baseado em emulação, um controlador por realimentação do erro de sincronização é dado a priori e a tarefa é calcular os parâmetros do gerador de eventos garantindo desempenho e estabilidade em malha fechada. Na abordagem de co-design, o gerador de eventos e a lei de controle são projetados simultaneamente. Resultados teóricos são obtidos para três tipos de mecanismo de geração de eventos (ETM), nomeadamente: estático, dinâmico e relaxado. Neste último caso, condições de sincronização prática são derivadas como uma forma de estabilidade ultimamente limitada. Para sintonizar os parâmetros da estratégia baseada em eventos, problemas de otimização são formulados visando reduzir o número de atualizações do sinal de controle (número de eventos) em relação a uma implementação time-triggered. Simulações numéricas são apresentadas para ilustrar a aplicação dos métodos propostos

Supervisory model predictive control of building integrated renewable and low carbon energy systems

To reduce fossil fuel consumption and carbon emission in the building sector, renewable and low carbon energy technologies are integrated in building energy systems to supply all or part of the building energy demand. In this research, an optimal supervisory controller is designed to optimize the operational cost and the CO2 emission of the integrated energy systems. For this purpose, the building energy system is defined and its boundary, components (subsystems), inputs and outputs are identified. Then a mathematical model of the components is obtained. For mathematical modelling of the energy system, a unified modelling method is used. With this method, many different building energy systems can be modelled uniformly. Two approaches are used; multi-period optimization and hybrid model predictive control. In both approaches the optimization problem is deterministic, so that at each time step the energy consumption of the building, and the available renewable energy are perfectly predicted for the prediction horizon. The controller is simulated in three different applications. In the first application the controller is used for a system consisting of a micro-combined heat and power system with an auxiliary boiler and a hot water storage tank. In this application the controller reduces the operational cost and CO2 emission by 7.31 percent and 5.19 percent respectively, with respect to the heat led operation. In the second application the controller is used to control a farm electrification system consisting of PV panels, a diesel generator and a battery bank. In this application the operational cost with respect to the common load following strategy is reduced by 3.8 percent. In the third application the controller is used to control a hybrid off-grid power system consisting of PV panels, a battery bank, an electrolyzer, a hydrogen storage tank and a fuel cell. In this application the controller maximizes the total stored energies in the battery bank and the hydrogen storage tank