A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Robust Observer Design for Takagi-Sugeno Fuzzy Systems with Mixed Neutral and Discrete Delays and Unknown Inputs

A robust observer design is proposed for Takagi-Sugeno fuzzy neutral models with unknown inputs. The model consists of a mixed neutral and discrete delay, and the disturbances are imposed on both state and output signals. Delay-dependent sufficient conditions for the design of an unknown input T-S observer with time delays are given in terms of linear matrix inequalities. Some relaxations are introduced by using intermediate variables. A numerical example is given to illustrate the effectiveness of the given results

Robust Fuzzy Observer-based Fault Detection for Nonlinear Systems

With the increasing demand for higher performance, safety and reliability of dynamic systems, fault diagnosis has received more and more attention. The observer-based strategy is one of the active research fields, which is widely used to construct model-based fault detection systems for technical processes which can be well modelled as linear time invariant systems. Fault diagnosis for nonlinear system is an active area of research. Observer-based fault detection includes two stages, residual generation and residual evaluation. The residual generation problems and residual evaluation problems for systems with only deterministic disturbances or stochastic disturbances have been widely separately studied. Recently some efforts have been made in the integrated design of fault detection systems for systems with deterministic disturbances and stochastic disturbances. Recently, successful results of applying Takagi-Sugeno (TS) fuzzy model-based technique to solve fault detection and isolation problems met in the nonlinear system have been achieved. With TS model, a nonlinear dynamic system can be linearised around a number of operating points. Each linear model represents the local system behaviour around the operating point. The global system behaviour is described by a fuzzy IF-THEN rules which represent local linear input/output relations of the nonlinear system. Applying the Takagi-Sugeno fuzzy model based technique to solve fault detection and isolation problems in the nonlinear systems is active area of research. The main contribution of this thesis is the design of robust fault detection systems based on Takagi-Sugeno fuzzy filters. There are a number of schemes to achieve robustness problem in fault detection. One of them is to introduce a performance index. It is function of unknown input signal and fault signal. For continuous time system, first, robust fault detection system will be designed for nonlinear system with only deterministic disturbance as unknown inputs. Second, robust fault detection system will be designed for nonlinear system with deterministic disturbance as unknown inputs and parameter uncertainties. Finally, robust fault detection system will be designed for nonlinear system with deterministic disturbance as unknown inputs and stated delay. Sufficient conditions for solving robustness problem are given in terms of Linear Matrix Inequalities (LMIs). For discrete time system, kalman filter design for nonlinear system is diffcult. In this thesis new fault detection approach will be presented for nonlinear system with only stochastic disturbance. Fault Detection (FD) system for each local subsystem is design by solving the corresponding Discrete-time Algebraic Riccati Equation (DARE). Optimisation algorithm based on minimizing the residual covariance matrix is used to obtain a robust FD system optimised for global system behaviour. The optimisation algorithm is established in terms of LMIs. The different robust fault diagnosis system are developed to detect sensor faults of vehicle lateral dynamic control systems

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

Altres ajuts: Acord transformatiu CRUE-CSICIn this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (TS) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks

A novel approach to fault detection for fuzzy stochastic systems with nonhomogeneous processes

In this paper, we consider a class of fuzzy stochastic systems with nonhomogeneous jump processes. Our focus is on the design of a fuzzy fault detection filter that is sensitive to faults but robust against unknown inputs. Furthermore, the error filtering system is stochastically stable. With reference to an H1 performance index and a new performance index, sufficient conditions to ensure the existence of a fuzzy robust fault detection filter are derived. Simulation studies are carried out, showing that the proposed fuzzy robust FD filter can rapidly detect the faults correctly

Health-aware predictive control schemes based on industrial processes

Aplicat embargament des de la data de defensa fins el dia 30 de desembre de 2021The research is motivated by real applications, such as pasteurization plant, water networks and autonomous system, which each of them require a specific control system to provide proper management able to take into account their particular features and operating limits in presence of uncertainties related to their operation and failures from component breakdowns. According to that most of the real systems have nonlinear behaviors, it can be approximated them by polytopic linear uncertain models such as Linear Parameter Varying (LPV) and Takagi-Sugeno (TS) models. Therefore, a new economic Model Predictive Control (MPC) approach based on LPV/TS models is proposed and the stability of the proposed approach is certified by using a region constraint on the terminal state. Besides, the MPC-LPV strategy is extended based on the system with varying delays affecting states and inputs. The control approach allows the controller to accommodate the scheduling parameters and delay change. By computing the prediction of the state variables and delay along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state and delay at each time instant. To increase the system reliability, anticipate the appearance of faults and reduce the operational costs, actuator health monitoring should be considered. Regarding several types of system failures, different strategies are studied for obtaining system failures. First, the damage is assessed with the rainflow-counting algorithm that allows estimating the component’s fatigue and control objective is modified by adding an extra criterion that takes into account the accumulated damage. Besides, two different health-aware economic predictive control strategies that aim to minimize the damage of components are presented. Then, economic health-aware MPC controller is developed to compute the components and system reliability in the MPC model using an LPV modeling approach and maximizes the availability of the system by estimating system reliability. Additionally, another improvement considers chance-constraint programming to compute an optimal list replenishment policy based on a desired risk acceptability level, managing to dynamically designate safety stocks in flowbased networks to satisfy non-stationary flow demands. Finally, an innovative health-aware control approach for autonomous racing vehicles to simultaneously control it to the driving limits and to follow the desired path based on maximization of the battery RUL. The proposed approach is formulated as an optimal on-line robust LMI based MPC driven from Lyapunov stability and controller gain synthesis solved by LPV-LQR problem in LMI formulation with integral action for tracking the trajectory.Esta tesis pretende proporcionar contribuciones teóricas y prácticas sobre seguridad y control de sistemas industriales, especialmente en la forma maten ática de sistemas inciertos. La investigación está motivada por aplicaciones reales, como la planta de pasteurización, las redes de agua y el sistema autónomo, cada uno de los cuales requiere un sistema de control específico para proporcionar una gestión adecuada capaz de tener en cuenta sus características particulares y limites o de operación en presencia de incertidumbres relacionadas con su operación y fallas de averías de componentes. De acuerdo con que la mayoría de los sistemas reales tienen comportamientos no lineales, puede aproximarse a ellos mediante modelos inciertos lineales politopicos como los modelos de Lineal Variación de Parámetros (LPV) y Takagi-Sugeno (TS). Por lo tanto, se propone un nuevo enfoque de Control Predictivo del Modelo (MPC) económico basado en modelos LPV/TS y la estabilidad del enfoque propuesto se certifica mediante el uso de una restricción de región en el estado terminal. Además, la estrategia MPC-LPV se extiende en función del sistema con diferentes demoras que afectan los estados y las entradas. El enfoque de control permite al controlador acomodar los parámetros de programación y retrasar el cambio. Al calcular la predicción de las variables de estado y el retraso a lo largo de un horizonte de tiempo de predicción, el modelo del sistema se puede modificar de acuerdo con la evaluación del estado estimado y el retraso en cada instante de tiempo. Para aumentar la confiabilidad del sistema, anticipar la aparición de fallas y reducir los costos operativos, se debe considerar el monitoreo del estado del actuador. Con respecto a varios tipos de fallas del sistema, se estudian diferentes estrategias para obtener fallas del sistema. Primero, el daño se evalúa con el algoritmo de conteo de flujo de lluvia que permite estimar la fatiga del componente y el objetivo de control se modifica agregando un criterio adicional que tiene en cuenta el daño acumulado. Además, se presentan dos estrategias diferentes de control predictivo económico que tienen en cuenta la salud y tienen como objetivo minimizar el daño de los componentes. Luego, se desarrolla un controlador MPC económico con conciencia de salud para calcular los componentes y la confiabilidad del sistema en el modelo MPC utilizando un enfoque de modelado LPV y maximiza la disponibilidad del sistema mediante la estimación de la confiabilidad del sistema. Además, otra mejora considera la programación de restricción de posibilidades para calcular una política ´optima de reposición de listas basada en un nivel de aceptabilidad de riesgo deseado, logrando designar dinámicamente existencias de seguridad en redes basadas en flujo para satisfacer demandas de flujo no estacionarias. Finalmente, un enfoque innovador de control consciente de la salud para vehículos de carreras autónomos para controlarlo simultáneamente hasta los límites de conducción y seguir el camino deseado basado en la maximización de la bacteria RUL. El diseño del control se divide en dos capas con diferentes escalas de tiempo, planificador de ruta y controlador. El enfoque propuesto está formulado como un MPC robusto en línea optimo basado en LMI impulsado por la estabilidad de Lyapunov y la síntesis de ganancia del controlador resuelta por el problema LPV-LQR en la formulación de LMI con acción integral para el seguimiento de la trayectoria.Postprint (published version

Advances in gain-scheduling and fault tolerant control techniques

This thesis presents some contributions to the state-of-the-art of the fields of gain-scheduling and fault tolerant control (FTC). In the area of gain-scheduling, the connections between the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms are analyzed, showing that the methods for the automated generation of models by nonlinear embedding and by sector nonlinearity, developed for one class of systems, can be easily extended to deal with the other class. Then, two measures, based on the notions of overboundedness and region of attraction estimates, are proposed in order to compare different models and choose which one can be considered the best one. Later, the problem of designing state-feedback controllers for LPV systems has been considered, providing two main contributions. First, robust LPV controllers that can guarantee some desired performances when applied to uncertain LPV systems are designed, by using a double-layer polytopic description that takes into account both the variability due to the varying parameter vector and the uncertainty. Then, the idea of designing the controller in such a way that the required performances are scheduled by the varying parameters is explored, which provides an elegant way to vary online the behavior of the closed-loop system. In both cases, the problem reduces to finding a solution to a finite number of linear matrix inequalities (LMIs), which can be done efficiently using the available solvers. In the area of fault tolerant control, the thesis first shows that the aforementioned double-layer polytopic framework can be used for FTC, in such a way that different strategies (passive, active and hybrid) are obtained depending on the amount of available information. Later, an FTC strategy for LPV systems that involves a reconfigured reference model and virtual actuators is developed. It is shown that by including the saturations in the reference model equations, it is possible to design a model reference FTC system that automatically retunes the reference states whenever the system is affected by saturation nonlinearities. In this way, a graceful performance degradation in presence of actuator saturations is incorporated in an elegant way. Finally, the problem of FTC of unstable LPV systems subject to actuator saturations is considered. In this case, the design of the virtual actuator is performed in such a way that the convergence of the state trajectory to zero is assured despite the saturations and the appearance of faults. Also, it is shown that it is possible to obtain some guarantees about the tolerated delay between the fault occurrence and its isolation, and that the nominal controller can be designed so as to maximize the tolerated delay.Aquesta tesi presenta diverses contribucions a l'estat de l'art del control per planificació del guany i del control tolerant a fallades (FTC). Pel que fa al control per planificació del guany, s'analitzen les connexions entre els paradigmes dels sistemes lineals a paràmetres variants en el temps (LPV) i de Takagi-Sugeno (TS). Es demostra que els mètodes per a la generació automàtica de models mitjançant encastament no lineal i mitjançant no linealitat sectorial, desenvolupats per una classe de sistemes, es poden estendre fàcilment per fer-los servir amb l'altra classe. Es proposen dues mesures basades en les nocions de sobrefitació i d'estimació de la regió d'atracció, per tal de comparar diferents models i triar quin d'ells pot ser considerat el millor. Després, es considera el problema de dissenyar controladors per realimentació d'estat per a sistemes LPV, proporcionant dues contribucions principals. En primer lloc, fent servir una descripció amb doble capa politòpica que té en compte tant la variabilitat deguda al vector de paràmetres variants i la deguda a la incertesa, es dissenyen controladors LPV robustos que puguin garantir unes especificacions desitjades quan s'apliquen a sistemes LPV incerts. En segon lloc, s'explora la idea de dissenyar el controlador de tal manera que les especificacions requerides siguin programades pels paràmetres variants. Això proporciona una manera elegant de variar en línia el comportament del sistema en llaç tancat. En tots dos casos, el problema es redueix a trobar una solució d'un nombre finit de desigualtats matricials lineals (LMIs), que es poden resoldre fent servir algorismes numèrics disponibles i molt eficients. En l'àrea del control tolerant a fallades, primerament la tesi mostra que la descripció amb doble capa politòpica abans esmentada es pot utilitzar per fer FTC, de tal manera que, en funció de la quantitat d'informació disponible, s'obtenen diferents estratègies (passiva, activa i híbrida). Després, es desenvolupa una estratègia de FTC per a sistemes LPV que fa servir un model de referència reconfigurat combinat amb la tècnica d'actuadors virtuals. Es mostra que mitjançant la inclusió de les saturacions en les equacions del model de referència, és possible dissenyar un sistema de control tolerant a fallades que resintonitza automàticament els estats de referència cada vegada que el sistema es veu afectat per les no linealitats de la saturació en els actuadors. D'aquesta manera s'incorpora una degradació elegant de les especificacions en presència de saturacions d'actuadors. Finalment, es considera el problema de FTC per sistemes LPV inestables afectats per saturacions d'actuadors. En aquest cas, es porta a terme el disseny de l'actuador virtual de tal manera que la convergència a zero de la trajectòria d'estat està assegurada tot i les saturacions i l'aparició de fallades. A més, es mostra que és possible obtenir garanties sobre el retard tolerat entre l'aparició d'una fallada i el seu aïllament, i que el controlador nominal es pot dissenyar maximitzant el retard tolerat

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