Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions

Esta tesis considera un enfoque basado en Lyapunov para el análisis y control de sistemas no lineales cuyas ecuaciones dinámicas son reescritas como un modelo Takagi-Sugeno o uno polinomial convexo. Estas estructuras permiten resolver problemas de control mediante técnicas de optimización convexa, más concretamente desigualdades matriciales lineales y suma de cuadrados, que son eficientes herramientas desde un punto de vista computacional. Después de proporcionar una visión general básica del estado actual en el campo de los modelos Takagi-Sugeno, esta tesis aborda cuestiones sobre las funciones de Lyapunov por trozos, dependiente de parámetros e integral de línea, con las siguientes contribuciones: Un algoritmo mejorado para estimaciones del dominio de atracción de sistemas no lineales para sistemas de tiempo continuo. Los resultados se basan en funciones de Lyapunov por trozos, desigualdades matriciales lineales y argumentaciones geométricas; enfoques basados en conjuntos de nivel en la literatura previa se han mejorado significativamente. Una función Lyapunov generalizada dependiente de parámetros para la síntesis de controladores para sistemas Takagi-Sugeno. El enfoque propone una ley de control multi-índice que retroalimenta la derivada del tiempo de las funciones de membresía del modelo Takagi-Sugeno para anular los términos que causan localidad a priori en el análisis de Lyapunov. Una nueva función integral de Lyapunov para el análisis de estabilidad de sistemas no lineales. Estos resultados generalizan aquellos basados en funciones de Lyapunov integral de línea al marco polinomial; resulta que los requisitos de independencia del camino pueden ser anulados por una definición adecuada de una función Lyapunov con términos integrales.This thesis considers a Lyapunov-based approach for analysis and control of nonlinear systems whose dynamical equations are rewritten as a Takagi-Sugeno model or a convex polynomial one. These structures allow solving control problems via convex optimisation techniques, more specifically linear matrix inequalities and sum-of-squares, which are efficient tools from the computational point of view. After providing a basic overview of the state of the art in the field of Takagi-Sugeno models, this thesis address issues on piecewise, parameter-dependent and line-integral Lyapunov functions, with the following contributions: An improved algorithm to estimate the domain of attraction of nonlinear systems for continuous-time systems. The results are based on piecewise Lyapunov functions, linear matrix inequalities, and geometrical argumentations; level-set approaches in prior literature are significantly improved. A generalised parameter-dependent Lyapunov function for synthesis of controllers for Takagi-Sugeno systems. The approach proposed a multi-index control law that feeds back the time derivative of the membership function of the Takagi-Sugeno model to cancel out the terms that cause a priori locality in the Lyapunov analysis. A new integral Lyapunov function for stability analysis of nonlinear systems. These results generalise those based on line-integral Lyapunov functions to the polynomial framework; it turns out path-independency requirements can be overridden by an adequate definition of a Lyapunov function with integral terms.Aquesta tesi considera un enfocament basat en Lyapunov per a l'anàlisi i control de sistemes no lineals les equacions dinàmiques dels quals són reescrites com un model Takagi-Sugeno o un de polinomial convex. Aquestes estructures permeten resoldre problemes de control mitjançant tècniques d'optimització convexa, més concretament desigualtats matricials lineals i suma de quadrats, que són eines eficients des d'un punt de vista computacional. Després de proporcionar una visió general bàsica de l'estat actual en el camp dels models Takagi-Sugeno, aquesta tesi aborda qüestions sobre les funcions de Lyapunov per trossos, dependent de paràmetres i integral de línia, amb les següents contribucions: Un algoritme millorat per a estimar el domini d'atracció de sistemes no lineals per a sistemes de temps continu. Els resultats es basen en funcions de Lyapunov per trossos, desigualtats matricials lineals i argumentacions geomètriques; enfocaments basats en conjunts de nivell en la literatura prèvia s'han millorat significativament. Una funció Lyapunov generalitzada dependent de paràmetres per a la síntesi de controladors per a sistemes Takagi-Sugeno. L'enfocament proposa una llei de control multi-índex que retroalimenta la derivada del temps de les funcions de membres del model Takagi-Sugeno per anul·lar els termes que causen localitat a priori en l'anàlisi de Lyapunov. Una nova funció integral de Lyapunov per a l'anàlisi d'estabilitat de sistemes no lineals. Aquests resultats generalitzen aquells basats en funcions de Lyapunov integral de línia al marc polinomial; resulta que els requisits d'independència del camí poden ser anul·lats per una definició adequada d'una funció Lyapunov amb termes integrals.González Germán, IT. (2018). Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/101282TESI

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results

An introduction to positive switched systems and their application to HIV treatment modeling

In the present work an introduction to positive switched systems is provided, along with an interesting application of this kind of systems to the biomededical area. Reflecting this twofold objective, the thesis is divided into two parts: in the first one classical theoretical aspects concerning positive switched systems are addressed by resorting to the Lyapunov function approach, while in the second part an application to the problem of drug treatment scheduling in HIV infection is presente

Constrained control using convex optimization

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1997.Includes bibliographical references (p. 113-121).by John Marc Shewchun.M.S

Stability analysis and controller design for switched time-delay systems

In this thesis, the stability analysis and control synthesis for uncertain switched time-delay systems are investigated. It is known that a wide variety of real-world systems are subject to uncertainty and also time-delay in their dynamics. These characteristics, if not taken into consideration in analysis and synthesis, can lead to important problems such as performance degradation or instability in a control system. On the other hand, the switching phenomenon often appears in numerous applications, where abrupt change is inevitable in the system model. Switching behavior in this type of systems can be triggered either by time, or by the state of the system. A theoretical framework to study various features of switched systems in the presence of uncertainty and time-delay (both neutral and retarded) would be of particular interest in important applications such as network control systems, power systems and communication networks. To address the problem of robust stability for the class of uncertain switched systems with unknown time-varying delay discussed above, sufficient conditions in the form of linear matrix inequalities (LMI) are derived. An adaptive switching control algorithm is then proposed for the stabilization of uncertain discrete time-delay systems subject to disturbance. It is assumed that the discrete time-delay system is highly uncertain, such that a single fixed controller cannot stabilize it effectively. Sufficient conditions are provided subsequently for the stability of switched time-delay systems with polytopic-type uncertainties. Moreover, an adaptive control scheme is provided to stabilize the uncertain neutral time-delay systems when the upper bounds on the system uncertainties are not available a priori . Simulations are provided throughout the thesis to support the theoretical result

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Identification and Optimal Linear Tracking Control of ODU Autonomous Surface Vehicle

Autonomous surface vehicles (ASVs) are being used for diverse applications of civilian and military importance such as: military reconnaissance, sea patrol, bathymetry, environmental monitoring, and oceanographic research. Currently, these unmanned tasks can accurately be accomplished by ASVs due to recent advancements in computing, sensing, and actuating systems. For this reason, researchers around the world have been taking interest in ASVs for the last decade. Due to the ever-changing surface of water and stochastic disturbances such as wind and tidal currents that greatly affect the path-following ability of ASVs, identification of an accurate model of inherently nonlinear and stochastic ASV system and then designing a viable control using that model for its planar motion is a challenging task. For planar motion control of ASV, the work done by researchers is mainly based on the theoretical modeling in which the nonlinear hydrodynamic terms are determined, while some work suggested the nonlinear control techniques and adhered to simulation results. Also, the majority of work is related to the mono- or twin-hull ASVs with a single rudder. The ODU-ASV used in present research is a twin-hull design having two DC trolling motors for path-following motion. A novel approach of time-domain open-loop observer Kalman filter identifications (OKID) and state-feedback optimal linear tracking control of ODU-ASV is presented, in which a linear state-space model of ODU-ASV is obtained from the measured input and output data. The accuracy of the identified model for ODU-ASV is confirmed by validation results of model output data reconstruction and benchmark residual analysis. Then, the OKID-identified model of the ODU-ASV is utilized to design the proposed controller for its planar motion such that a predefined cost function is minimized using state and control weighting matrices, which are determined by a multi-objective optimization genetic algorithm technique. The validation results of proposed controller using step inputs as well as sinusoidal and arc-like trajectories are presented to confirm the controller performance. Moreover, real-time water-trials were performed and their results confirm the validity of proposed controller in path-following motion of ODU-ASV

Contributions to road safety: from abstractions and control theory to real solutions, discussion and evaluation

This manuscript aims to describe my career in the transportation domain, putting in evidence my contributions in different levels, as for example thesis advising, teaching, research animation and coordination, projects construction and participation in expert committees, among others, besides my scientific research itself. The goal, besides the HDR diploma itself, is to show very clearly, including to myself, this 'pack' of contributions in order to look for better contributions to the transportation and control communities or to other communities in the future, and also which research directions I will define to work on in the following. I obtained my PhD degree in the Laboratoire des Signaux et Systèmes - L2S 1 in collaboration with MIT, in 2001, having worked in a purely theoretical automatic control topic scarcely known in the literature - the adaptive control of systems with nonlinear parameterization problem. Arriving in 2002 as a permanent researcher to the former LCPC (Laboratoire Central des Ponts et haussées), now called IFSTTAR (Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux), I have been faced to real problems to solve in practice, and faced to the new community of transportation, with a completely different philosophy of work. I have nowadays this double vision - of the very applied transportation domain with concrete problems to be solved that touch the citizen every day, and the vision of a very rich high-level theoretical research in automatic control with powerful tools to solve the real problems, or on the other hand, with control problems that appear because of the need for new tools to solve the real problems. I consider this as an important characteristic for my future contributions. Besides the knowledge in Transportation itself, my eleven years of career in IFSTTAR gave me as well the following new features : 1. From the individual research, I have learned also how to coordinate work (in projects for example, as in the PReVAL sub-project of the European PReVENT project, in which I co-leaded one workpackage, or for research teams, as the control team of LIVIC, coordinated by myself from 2006 to 2009). I have also learned how to animate research (by coordinating research working groups or organizing scientific events and workshops - see for example the working group RSEI and the related scientific event below that I have organized in June 2012) and how to advise students. 2. Besides the double vision I have described above, the experience gave me also the acquisition of a quite multidisciplinary view of the problems in the domain. Firstly, arriving in LIVIC, in the frame of the French consortium ARCOS, I have worked for two years in close cooperation with experts in cognitive sciences (the PsyCoTech group from IRCCyN, Nantes) on designing driving assistance systems to a human driver. After this work, I have continued the collaboration with experts in human sciences within the PReVAL subproject of PReVENT on driving assistance systems evaluation and within the French ANR PARTAGE project, that I have constructed together with the PsyCoTec team of IRCCyN and leaded the IFSTTAR partner for one year. In a dition, through my participation in PReVENT at dirent levels (in two meetings of the Core Group, in PReVAL by co-leading the workpackage 3 on Technical Evaluation of ADAS - ADAS is the shortcut for Advanced Driving Assistance Systems - and in the SAFELANE subproject), I have learned many different aspects of ITS systems. I consider this as an add-on value for my 'pack of knowledge'. 3. What I call "from abstractions to real problems : coming back and forth to solve these real problems" has been matured in my mind, and I am very grateful to my students, with whom I have learned and that helped me in this maturing process. By this sentence, I mean, with a problem to solve in hands, and after building an abstraction, or a simplified view of the problem, and the design of a solution, how to apply it, and to come back again to the theory to change it and to come back to the practice, and so on. This is exactly one of the pillars of the NoE HYCON2, for making interact the theory with the application domains. 4. Considering a problem inserted into the societal context, or inserted within its related context, has been another maturing for myself that I consider very important, notably in the transportation domain, that represents a very complex context containing many different parameters, scenarios and objectives and in addition all the uncertainties linked to the human behavior. I think that it is very important to have a very large view of the context in which the specific problem we are treating is placed. Without this, one cannot say in most of the cases, from my point of view, that the problem is solved. This point will be discussed in Chapter 9.5. 5. Another point that I consider important and where I have been contributing recently is the road mapping work. The acquisition of the multidisciplinary knowledge and a larger view of the domain that I have mentioned in the preceding items, together with my theoretical knowledge in automatic control, allowed myself to start contributing to theroad mapping work in Transportation (through my participation in the imobility forum, in HYCON2 and the in the support action T-Area-SoS on Systems of Systems - all these actions to give advice to the European Commission on the priority areas to be considered in the new Calls, notably in the frame of the H2020 program). I had also the pleasure of opening again books and thesis that I had studied in my PhD work, this time now for advising students in the frame of other very different problems. The very beautiful thesis of Mikael Johansson, Lund University, on piecewise linear systems stability theory is an example. My previous study on switched systems, and the implication of switched Lyapunov functions on stability helped me also in advising my students (Post-Docs, PhD, and M.Sc. students), this time for real applications, with very interesting results blooming up from their work. I realize also that the experience that I have described in the five items above must be put in favor of students since this kind of knowledge cannot be found in the books. Concluding, in these last eleven years, from 2002 to 2013, I could bring to the scientic community and to my students a set of contributions of different kinds. I will try to make clear these contributions for the reader in the next two chapters (written in English and in French). This document is organized in the following way : Part II contains my complete curriculum vitae (in french) where all these contributions will be described in detail. Part III contains then the scientific contributions of the manuscript. What I aim in this chapter is to describe, but further, to analyze them with a distanced look and providing a critical view, announcing perspectives, and placing and discussing the obtained results in the societal context. This is in straight relation with item 4 above. Also, I prefer to adopt, as far as possible, a form comprehensible to the non-automatic control expert, with, as far as possible as well, qualitative explanations and then appropriated references containing the theorems and the definitions corresponding to the qualitative explanations will be provided. In the case it is necessary, they are provided within the text. The Part III is structured in the following chapters. Chapter 8 contains an overview of the global transportation scenario with the associated challenges and a description of the driving assistance systems context. Chapter 9 contains my scientific contributions. These include my research results, my contributions in students advising, in the coordination of research groups, and the collaborative works. It is structured in 3 sections : Section 9.1 introduces what will be the greed for a part of the main contributions, that are described in Sections 9.2 and 9.3. Section 9.1 is also dedicated to showing to the reader how theory and abstractions can be very important for solving real problems. Chapter 9.4 describes other contributions that are the result of collaborative works. A discussion from a multidisciplinary view is provided in Chapter 9.5 based on a survey paper of myself. Chapter 10 will be finally dedicated to the perspectives and the general conclusions. Then last Part contains as annexes a selection of the publications that I consider the most illustrative of my contributions described in Chapter 9. Finally, since the described work is in the intersection of two communities - the transportation and the control theory communities - I decided to write a part of the document dedicated to the non control experts readers. This is Part VI of the document whose aim is to provide some fundamental notions on control theory in a very simple qualitative description whose understanding will help the different readers to understand the contributions

A Dynamical System-based Approach to Modeling Stable Robot Control Policies via Imitation Learning

Despite tremendous advances in robotics, we are still amazed by the proficiency with which humans perform movements. Even new waves of robotic systems still rely heavily on hardcoded motions with a limited ability to react autonomously and robustly to a dynamically changing environment. This thesis focuses on providing possible mechanisms to push the level of adaptivity, reactivity, and robustness of robotic systems closer to human movements. Specifically, it aims at developing these mechanisms for a subclass of robot motions called “reaching movements”, i.e. movements in space stopping at a given target (also referred to as episodic motions, discrete motions, or point-to-point motions). These reaching movements can then be used as building blocks to form more advanced robot tasks. To achieve a high level of proficiency as described above, this thesis particularly seeks to derive control policies that: 1) resemble human motions, 2) guarantee the accomplishment of the task (if the target is reachable), and 3) can instantly adapt to changes in dynamic environments. To avoid manually hardcoding robot motions, this thesis exploits the power of machine learning techniques and takes an Imitation Learning (IL) approach to build a generic model of robot movements from a few examples provided by an expert. To achieve the required level of robustness and reactivity, the perspective adopted in this thesis is that a reaching movement can be described with a nonlinear Dynamical System (DS). When building an estimate of DS from demonstrations, there are two key problems that need to be addressed: the problem of generating motions that resemble at best the demonstrations (the “how-to-imitate” problem), and most importantly, the problem of ensuring the accomplishment of the task, i.e. reaching the target (the “stability” problem). Although there are numerous well-established approaches in robotics that could answer each of these problems separately, tackling both problems simultaneously is challenging and has not been extensively studied yet. This thesis first tackles the problem mentioned above by introducing an iterative method to build an estimate of autonomous nonlinear DS that are formulated as a mixture of Gaussian functions. This method minimizes the number of Gaussian functions required for achieving both local asymptotic stability at the target and accuracy in following demonstrations. We then extend this formulation and provide sufficient conditions to ensure global asymptotic stability of autonomous DS at the target. In this approach, an estimation of the underlying DS is built by solving a constraint optimization problem, where the metric of accuracy and the stability conditions are formulated as the optimization objective and constraints, respectively. In addition to ensuring convergence of all motions to the target within the local or global stability regions, these approaches offer an inherent adaptability and robustness to changes in dynamic environments. This thesis further extends the previous approaches and ensures global asymptotic stability of DS-based motions at the target independently of the choice of the regression technique. Therefore, it offers the possibility to choose the most appropriate regression technique based on the requirements of the task at hand without compromising DS stability. This approach also provides the possibility of online learning and using a combination of two or more regression methods to model more advanced robot tasks, and can be applied to estimate motions that are represented with both autonomous and non-autonomous DS. Additionally, this thesis suggests a reformulation to modeling robot motions that allows encoding of a considerably wider set of tasks ranging from reaching movements to agile robot movements that require hitting a given target with a specific speed and direction. This approach is validated in the context of playing the challenging task of minigolf. Finally, the last part of this thesis proposes a DS-based approach to realtime obstacle avoidance. The presented approach provides a modulation that instantly modifies the robot’s motion to avoid collision with multiple static and moving convex obstacles. This approach can be applied on all the techniques described above without affecting their adaptability, swiftness, or robustness. The techniques that are developed in this thesis have been validated in simulation and on different robotic platforms including the humanoid robots HOAP-3 and iCub, and the robot arms KATANA, WAM, and LWR. Throughout this thesis we show that the DS-based approach to modeling robot discrete movements can offer a high level of adaptability, reactivity, and robustness almost effortlessly when interacting with dynamic environments