A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm

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

Commande dynamique de robots déformables basée sur un modèle numérique

This work focuses on modeling and control of soft robots. It covers the entire development of the controller, from the modeling step to the practical experimental validation.From a theoretical point a view, large-scale dynamical systems along with model reduction algorithms are studied. In addition to the theoretical studies, different experimental setups are used to illustrate the results. A cable-driven soft robot and a pressurized soft arm are used to test the control algorithms. Through these different setups, we show that the method can handle different types of actuation, different geometries and mechanical properties. This emphasizes one of the interests of the method, its genericity.Cette thèse s'intéresse à la modélisation et à la commande de robots déformables (robots dont le mouvement se fait par déformation). Nous nous intéressons à la conception de lois de contrôle en boucle fermée répondant aux besoins spécifiques du contrôle dynamique de ces robots, sans restrictions fortes sur leur géométrie. La résolution de ce défi soulève des questions théoriques qui nous amènent au deuxième objectif de cette thèse: développer de nouvelles stratégies pour étudier les systèmes de grandes dimensions

Identification of low order models for large scale processes

Many industrial chemical processes are complex, multi-phase and large scale in nature. These processes are characterized by various nonlinear physiochemical effects and fluid flows. Such processes often show coexistence of fast and slow dynamics during their time evolutions. The increasing demand for a flexible operation of a complex process, a pressing need to improve the product quality, an increasing energy cost and tightening environmental regulations make it rewarding to automate a large scale manufacturing process. Mathematical tools used for process modeling, simulation and control are useful to meet these challenges. Towards this purpose, development of process models, either from the first principles (conservation laws) i.e. the rigorous models or the input-output data based models constitute an important step. Both types of models have their own advantages and pitfalls. Rigorous process models can approximate the process behavior reasonably well. The ability to extrapolate the rigorous process models and the physical interpretation of their states make them more attractive for the automation purpose over the input-output data based identified models. Therefore, the use of rigorous process models and rigorous model based predictive control (R-MPC) for the purpose of online control and optimization of a process is very promising. However, due to several limitations e.g. slow computation speed and the high modeling efforts, it becomes difficult to employ the rigorous models in practise. This thesis work aims to develop a methodology which will result in smaller, less complex and computationally efficient process models from the rigorous process models which can be used in real time for online control and dynamic optimization of the industrial processes. Such methodology is commonly referred to as a methodology of Model (order) Reduction. Model order reduction aims at removing the model redundancy from the rigorous process models. The model order reduction methods that are investigated in this thesis, are applied to two benchmark examples, an industrial glass manufacturing process and a tubular reactor. The complex, nonlinear, multi-phase fluid flow that is observed in a glass manufacturing process offers multiple challenges to any model reduction technique. Often, the rigorous first principle models of these benchmark examples are implemented in a discretized form of partial differential equations and their solutions are computed using the Computational Fluid Dynamics (CFD) numerical tools. Although these models are reliable representations of the underlying process, computation of their dynamic solutions require a significant computation efforts in the form of CPU power and simulation time. The glass manufacturing process involves a large furnace whose walls wear out due to the high process temperature and aggressive nature of the molten glass. It is shown here that the wearing of a glass furnace walls result in change of flow patterns of the molten glass inside the furnace. Therefore it is also desired from the reduced order model to approximate the process behavior under the influence of changes in the process parameters. In this thesis the problem of change in flow patterns as result of changes in the geometric parameter is treated as a bifurcation phenomenon. Such bifurcations exhibited by the full order model are detected using a novel framework of reduced order models and hybrid detection mechanisms. The reduced order models are obtained using the methods explained in the subsequent paragraphs. The model reduction techniques investigated in this thesis are based on the concept of Proper Orthogonal Decompositions (POD) of the process measurements or the simulation data. The POD method of model reduction involves spectral decomposition of system solutions and results into arranging the spatio-temporal data in an order of increasing importance. The spectral decomposition results into spatial and temporal patterns. Spatial patterns are often known as POD basis while the temporal patterns are known as the POD modal coefficients. Dominant spatio-temporal patterns are then chosen to construct the most relevant lower dimensional subspace. The subsequent step involves a Galerkin projection of the governing equations of a full order first principle model on the resulting lower dimensional subspace. This thesis can be viewed as a contribution towards developing the databased nonlinear model reduction technique for large scale processes. The major contribution of this thesis is presented in the form of two novel identification based approaches to model order reduction. The methods proposed here are based on the state information of a full order model and result into linear and nonlinear reduced order models. Similar to the POD method explained in the previous paragraph, the first step of the proposed identification based methods involve spectral decomposition. The second step is different and does not involve the Galerkin projection of the equation residuals. Instead, the second step involves identification of reduced order models to approximate the evolution of POD modal coefficients. Towards this purpose, two different methods are presented. The first method involves identification of locally valid linear models to represent the dynamic behavior of the modal coefficients. Global behavior is then represented by ‘blending’ the local models. The second method involves direct identification of the nonlinear models to represent dynamic evolution of the model coefficients. In the first proposed model reduction method, the POD modal coefficients, are treated as outputs of an unknown reduced order model that is to be identified. Using the tools from the field of system identification, a blackbox reduced order model is then identified as a linear map between the plant inputs and the modal coefficients. Using this method, multiple local reduced LTI models corresponding to various working points of the process are identified. The working points cover the nonlinear operation range of the process which describes the global process behavior. These reduced LTI models are then blended into a single Reduced Order-Linear Parameter Varying (ROLPV) model. The weighted blending is based on nonlinear splines whose coefficients are estimated using the state information of the full order model. Along with the process nonlinearity, the nonlinearity arising due to the wear of the furnace wall is also approximated using the RO-LPV modeling framework. The second model reduction method that is proposed in this thesis allows approximation of a full order nonlinear model by various (linear or nonlinear) model structures. It is observed in this thesis, that, for certain class of full order models, the POD modal coefficients can be viewed as the states of the reduced order model. This knowledge is further used to approximate the dynamic behavior of the POD modal coefficients. In particular, reduced order nonlinear models in the form of tensorial (multi-variable polynomial) systems are identified. In the view of these nonlinear tensorial models, the stability and dissipativity of these models is investigated. During the identification of the reduced order models, the physical interpretation of the states of the full order rigorous model is preserved. Due to the smaller dimension and the reduced complexity, the reduced order models are computationally very efficient. The smaller computation time allows them to be used for online control and optimization of the process plant. The possibility of inferring reduced order models from the state information of a full order model alone i.e. the possibility to infer the reduced order models in the absence of access to the governing equations of a full order model (as observed for many commercial software packages) make the methods presented here attractive. The resulting reduced order models need further system theoretic analysis in order to estimate the model quality with respect to their usage in an online controller setting

Active Suppression ofAerofoil Flutter via Neural-Network-Based Adaptive Nonlinear Optimal Control

This thesis deals with active flutter suppression (AFS) on aerofoils via adaptive nonlinear optimal control using neural networks (NNs). Aeroelastic flutter can damage aerofoils if not properly controlled. AFS not only ensures flutter-free flight but also enables the use of aerodynamically more efficient lightweight aerofoils. However, existing optimal controllers for AFS are generally susceptible to modelling errors while other controllers less prone to uncertainties do not provide optimal control. This thesis, thus, aims to reduce the impact of the dilemma by proposing new solutions based on nonlinear optimal control online synthesis (NOCOS) according to online updated dynamics. Existing NOCOS methods, with NNs as essential elements, require a separate initial stabilising control law for the overall system, an additional stabilising tuning loop for the actor NN, or an additional stabilising term in the critic NN tuning law, to guarantee the closed-loop stability for unstable and marginally stable systems. The resulting complexity is undesired in AFS applications due to computational concerns in real-time implementation. Moreover, the existing NOCOS methods are confined to locally nonlinear systems, while aeroelastic systems under consideration are globally nonlinear. These make all the existing NOCOS algorithms inapplicable to AFS without modification and improvement. Therefore, this thesis solves the aforementioned problems through the following step-by-step approaches. Firstly, a four degrees-of-freedom (4-DOF) aeroelastic model is considered, where leading- and trailing-edge control surfaces of the aerofoil are used to actively suppress flutter. Accordingly, a virtual stiffness-damping system (VSDS) is developed to simulate physical stiffness in the aeroelastic system. The VSDS, together with a scaled-down typical aerofoil section placed in a wind tunnel, serve as an experimental 4-DOF aeroelastic test-bed for synthesis and validation of proposed AFS controllers that follow. Secondly, a Modified form of NN-based Value Function Approximation (MVFA), tuned by gradient-descent learning, is proposed for NOCOS to address the closedloop stability in a compact controller configuration suitable for real-time implementation. Its validity and efficacy are examined by the Lyapunov stability analysis and numerical studies. Thirdly, a systematic procedure based on linear matrix inequalities is further proposed for synthesising a scheduled parameter matrix to generalise the MVFA to to globally nonlinear cases, so that the new NN controller suits AFS applications. In addition, the extended Kalman filter (EKF) is proposed for the new NN controller for fast parameter convergence. An identifier NN is also derived to capture and update aeroelastic dynamics in real time to mitigate the impact of modelling errors. Wind-tunnel experiments were conducted for validation. Finally, a non-quadratic functional is introduced to generalise the performance index to tackle the problem where control inputs are constrained. The feasibility of including the non-quadratic cost function under the proposed control scheme based on the MVFA is examined via the Lyapunov stability analysis and was also experimentally evaluated through the wind-tunnel testings. The proposed NN controllers are compact in structure and shown capable of maintaining the closed-loop stability while eliminating the need for a separate initial stabilising control law for the overall system, an additional tuning loop for the actor NN, and an additional stabilising term in the critic NN tuning law. Under the new control schemes, online synthesised nonlinear control laws are optimal in the cases with and without constraints in control. Comparisons drawn with a popular linear-parameter-varying (LPV) controller in the form of the widely used linear quadratic regulator (LQR) in experiments show that the proposed NN controllers outperform the LPV-LQR algorithm and improve AFS from the optimal control perspective. Specifically, the proposed NN controllers can effectively mitigate the impact of modelling errors, successfully solving the mentioned dilemma involved in AFS. The results also confirm that the proposed NN controllers are suitable for real-time implementation.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 201

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

Model-based Reinforcement Learning of Nonlinear Dynamical Systems

Model-based Reinforcement Learning (MBRL) techniques accelerate the learning task by employing a transition model to make predictions. In this dissertation, we present novel techniques for online learning of unknown dynamics by iteratively computing a feedback controller based on the most recent update of the model. Assuming a structured continuous-time model of the system in terms of a set of bases, we formulate an infinite horizon optimal control problem addressing a given control objective. The structure of the system along with a value function parameterized in the quadratic form provides flexibility in analytically calculating an update rule for the parameters. Hence, a matrix differential equation of the parameters is obtained, where the solution is used to characterize the optimal feedback control in terms of the bases, at any time step. Moreover, the quadratic form of the value function suggests a compact way of updating the parameters that considerably decreases the computational complexity. In the convergence analysis, we demonstrate asymptotic stability and optimality of the obtained learning algorithm around the equilibrium by revealing its connections with the analogous Linear Quadratic Regulator (LQR). Moreover, the results are extended to the trajectory tracking problem. Assuming a structured unknown nonlinear system augmented with the dynamics of a commander system, we obtain a control rule minimizing a given quadratic tracking objective function. Furthermore, in an alternative technique for learning, a piecewise nonlinear affine framework is developed for controlling nonlinear systems with unknown dynamics. Therefore, we extend the results to obtain a general piecewise nonlinear framework where each piece is responsible for locally learning and controlling over some partition of the domain. Then, we consider the Piecewise Affine (PWA) system with a bounded uncertainty as a special case, for which we suggest an optimization-based verification technique. Accordingly, given a discretization of the learned PWA system, we iteratively search for a common piecewise Lyapunov function in a set of positive definite functions, where a non-monotonic convergence is allowed. Then, this Lyapunov candidate is verified for the uncertain system. To demonstrate the applicability of the approaches presented in this dissertation, simulation results on benchmark nonlinear systems are included, such as quadrotor, vehicle, etc. Moreover, as another detailed application, we investigate the Maximum Power Point Tracking (MPPT) problem of solar Photovoltaic (PV) systems. Therefore, we develop an analytical nonlinear optimal control approach that assumes a known model. Then, we apply the obtained nonlinear optimal controller together with the piecewise MBRL technique presented previously

Nonquadratic Lyapunov function for continuous TS fuzzy models through their discretization

[IF=1.986]International audienceSince the beginning of the fuzzy control theory, results have been obtained independently for continuous and discrete models. It is still quite difficult to use nonquadratic Lyapunov functions for the continuous case, while this is much easier for the discrete case. This approach tries to put a bridge between the continuous and discrete cases for the class of continuous Takagi Sugeno fuzzy models that can be exactly discretized. Indeed, for this particular class, once the stability of the discrete model is ensured, the same control law applied to the continuous model will ensure the stability too. The interest of such an approach is that complex control laws and complex Lyapunov functions can be easily used. Simulation examples show that stabilizing feedbacks may be obtained with discrete control laws when purely continuous ones fail

Dynamic Incentives for Optimal Control of Competitive Power Systems

Technologisch herausfordernde Transformationsprozesse wie die Energiewende können durch passende Anreizsysteme entscheidend beschleunigt werden. Ziel solcher Anreize ist es hierbei, ein Umfeld idealerweise so zu schaffen, dass das Zusammenspiel aller aus Sicht der beteiligten Wettbewerber individuell optimalen Einzelhandlungen auch global optimal im Sinne eines übergeordneten Großziels ist. Die vorliegende Dissertation schafft einen regelungstechnischen Zugang zur Frage optimaler Anreizsysteme für heutige und zukünftige Stromnetze im Zieldreieck aus Systemstabilität, ökonomischer Effizienz und Netzdienlichkeit. Entscheidende Neuheit des entwickelten Ansatzes ist die Einführung zeitlich wie örtlich differenzierter Echtzeit-Preissignale, die sich aus der Lösung statischer und dynamischer Optimierungsprobleme ergeben. Der Miteinbezug lokal verfügbarer Messinformationen, die konsequente Mitmodellierung des unterlagerten physikalischen Netzes inklusive resistiver Verluste und die durchgängig zeitkontinuierliche Formulierung aller Teilsysteme ebnen den Weg von einer reinen Anreiz-Steuerung hin zu einer echten Anreiz-Regelung. Besonderes Augenmerk der Arbeit liegt in einer durch das allgemeine Unbundling-Gebot bedingten rigorosen Trennung zwischen Markt- und Netzakteuren. Nach umfangreicher Analyse des hierbei entstehenden geschlossenen Regelkreises erfolgt die beispielhafte Anwendung der Regelungsarchitektur für den Aufbau eines neuartigen Echtzeit-Engpassmanagementsystems. Weitere praktische Vorteile des entwickelten Ansatzes im Vergleich zu bestehenden Konzepten werden anhand zweier Fallstudien deutlich. Die port-basierte Systemmodellierung, der Verzicht auf zentralisierte Regeleingriffe und nicht zuletzt die Möglichkeit zur automatischen, dezentralen Selbstregulation aller Preise über das Gesamtnetz hinweg stellen schließlich die problemlose Erweiterbarkeit um zusätzliche optionale Anreizkomponenten sicher