A novel system identification (SI)-based structural health assessment (SHA) procedure has been developed integrating several theoretical and implementation aspects. The procedure assesses health of structures using limited noise-contaminated dynamic responses and without using input excitation information. Since most practical structures are three dimensional (3D), the procedure has been developed for general 3D structures, represented by finite elements (FEs). The procedure identifies defects by tracking the changes in the stiffness of the elements in the FE representation. Once a defective element is identified, defect spot can be identified accurately within the defective element. The procedure is denoted as 3D Generalized Iterative Least-Squares Extended Kalman Filter with Unknown Input (3D GILS-EKF-UI) and implemented in two stages. In Stage 1, based on the available responses, substructure(s) are selected and the 3D GILS-UI procedure is used to generate the unknown input excitation, stiffness parameters of the elements in the substructure, and two Rayleigh damping coefficients. Using information from Stage 1, stiffness parameters for the whole structure are identified using EKF with Weighted Global Iteration (EKF-WGI) in Stage 2. The procedure accurately identified defect-free and defective states of various 3D structures using only analytically generated limited responses. To increase the robustness, 3D GILS-EKF-UI has been extended to develop an integrated structural health assessment strategy, denoted as Iterative Least-Squares Extended Kalman Filter with Unknown Input and Advanced Digital Integration Technique (ILS-EKF-UI-ADIT). The procedure has been implemented in three stages. In Stage 1, an advanced digital integration technique (ADIT) is implemented for post-processing of noise-contaminated acceleration time-histories, addressing all major challenges of digital integration. It also overcomes non-convergence issue in Stage 2 that arises due to phase-shift and amplitude errors. In Stage 2, substructure(s) are identified using the least-squares procedure. In Stage 3, stiffness parameters for the whole structure are identified using the EKF-WGI procedure. ILS-EKF-UI-ADIT has been verified in presence of relatively large noise in the acceleration time-histories, measured at small part(s) of defect-free and defective structures, without using excitation information. The SHA procedure is robust and has the potential to be applied for the health assessment, maintenance, retrofitting, and life extension of existing structural systems.

The problem of distributed state estimation over a sensor network in which a set of nodes collaboratively estimates the state of continuous-time linear systems is considered. Distributed estimation strategies improve estimation and robustness of the sensors to environmental obstacles and sensor failures in a sensor network. In particular, this dissertation focuses on the benefits of weight adaptation of the interconnection gains in distributed Kalman filters, distributed unknown input observers, and distributed functional observers. To this end, an adaptation strategy is proposed with the adaptive laws derived via a Lyapunov-redesign approach. The justification for the gain adaptation stems from a desire to adapt the pairwise difference of estimates as a function of their agreement, thereby enforcing an interconnection-dependent gain. In the proposed scheme, an adaptive gain for each pairwise difference of the interconnection terms is used in order to address edge-dependent differences in the estimates. Accounting for node-specific differences, a special case of the scheme is presented where it uses a single adaptive gain in each node estimate and which uniformly penalizes all pairwise differences of estimates in the interconnection term. In the case of distributed Kalman filters, the filter gains can be designed either by standard Kalman or Luenberger observers to construct the adaptive distributed Kalman filter or adaptive distributed Luenberger observer. Stability of the schemes has been shown and it is independent of the graph topology and therefore the schemes are applicable to both directed and undirected graphs. The proposed algorithms offer a significant reduction in communication costs associated with information flow by the nodes compared to other distributed Kalman filters. Finally, numerical studies are presented to illustrate the performance and effectiveness of the proposed adaptive distributed Kalman filters, adaptive distributed unknown input observers, and adaptive distributed functional observers.

An unknown input observer provides perfect asymptotic tracking of the state of a system affected by unknown inputs. Such an observer exists (possibly requiring a delay in estimation) if and only if the system satisfies a property known as strong detectability. In this thesis, we consider the problem of selecting (at design-time) a minimum cost subset of sensors from a given set to make a given system strongly detectable. We show this problem is NP-hard even when the system is stable. Furthermore, we show it is not possible to approximate the minimum cost within a factor of log(n) in polynomial-time (unless P=NP). However, we prove if a given system (with a selected set of sensors) is already strongly detectable, finding the smallest set of additional sensors to install to obtain a zero-delay observer can be done in polynomial time. Next we consider the problem of attacking a set of deployed sensors to remove the property of strong detectability. We show finding the smallest number of sensors to remove is NP-hard. Lastly through simulations, we analyze two greedy approaches for approximating the strong detectability sensor selection problem.

<div>Cyber-Physical Systems (CPSs) consist of physical and computational components usually interconnected through the internet. This type of systems have found applications in robotic surgery, smart medical services, driverless cars, smart power grids as well as in modern homes and offices. For a CPS to function properly, a reliable and secure communications between the system physical and cyber elements is of utmost importance. Malicious attacks during control signals and output measurements transmission between the physical plant and the control center must be addressed, which is the main research problem studied in this thesis.</div><div><br></div><div>A novel robust observer was proposed to synthesize a combined controller-observer compensator for a class of CPSs with sparse malicious attacks and arbitrary disturbances. The compensator consists of a controller, a norm approximator, and an unknown input observer (UIO). The proposed observer was compared with a norm-based observer given in the literature to show its advantage. To further enhance the proposed observer's performance against arbitrary disturbances, design methods were given that use fictitious output measurements and error correcting code (ECC) approach. The design of the UIO was extended to a bank of UIOs in order to improve the observer's performance against sparse malicious attacks.</div><div><br></div><div>The proposed observer can be used in the design of UIO-based fault detection and isolation (FDI) algorithms as well as in the distributed fault-tolerant control of large-scale interconnected systems. The results of this thesis can be applied to the design of controller-observer compensators for CPSs with modeling uncertainties.</div>

Current consumption measurements are useful in a wide variety of applications, including power monitoring and fault detection within a lithium battery management system (BMS). This measurement is typically taken using either a shunt resistor or a Hall-effect current transducer. Although both methods have achieved accurate current measurements, shunt resistors have inherent power loss and often require isolation circuitry, and Hall-effect sensors are generally expensive. This work explores a novel alternative to sensing battery current by measuring terminal voltages and cell temperatures and using an unknown input observer (UIO) to estimate the battery current. An accurate model of a LiFePO4 cell is created and is then used to characterize a model of the proposed current estimation technique. Finally, the current estimation technique is implemented in hardware and tested in an online BMS environment. Results show that the current estimation technique is sufficiently accurate for a variety of applications including fault detection and power profiling.

A novel structural health assessment (SHA) technique is proposed. It is a finite element-based time domain nonlinear system identification technique. The procedure is developed in two stages to incorporate several desirable features and increase its implementation potential. First, a weighted global iteration with an objective function is introduced in the unscented Kalman filter (UKF) procedure in order to obtain stable, convergent, and optimal solution. Furthermore, it also improves the capability of the UKF procedure to identify a large structural system using only a short duration of responses measured at a limited number of dynamic degrees of freedom (DDOFs). The combined procedure is denoted as unscented Kalman filter with weighted global iteration (UKF-WGI). Then, UKF-WGI is integrated with iterative least-squares with unknown input (ILS-UI) in order to increase its implementation potential. The substructure concept is also incorporated in the procedure. The integrated procedure is denoted as unscented Kalman filter with unknown input and weighted global iteration (UKF-UI-WGI). The two most important features of the method are that it does not need information on input excitation and uses only limited number of noise-contaminated response information to identify structural systems. Also, the method is able to identify the defects at the local element level by tracking the changes in the stiffness of the structural elements in the finite element representation. The UKF-UI-WGI procedure is implemented in two stages. In Stage 1, based on the location of input excitation, the substructure is selected. Using only responses at all DDOFs in the substructure, ILS-UI can identify the input excitation time-histories, stiffness parameters of all the elements in the substructure, and two Rayleigh damping coefficients. The outcomes of the first stage are necessary to initiate UKF-WGI. Using the information from Stage 1, the stiffness parameters of all the elements in the structure are identified using UKF-WGI in Stage 2. To demonstrate the effectiveness of the procedure, health assessment of relatively large structural systems is presented. Small and relatively large defects are introduced at different locations in the structure and the capability of the method to detect the health of the structure is examined. The optimum number and location of measured responses are also investigated. It is demonstrated that the method is capable of identifying defect-free and defective states of the structures using minimum information. Furthermore, it can locate defect spot within a defective element accurately. The comparative studies are also conducted between the proposed methods and available methods in the literature. First, it is between the UKF-WGI and extended Kalman filter with weighted global iteration (EKF-WGI) procedure. Then, it is between UKF-UI-WGI and generalized iterative least-squares extended Kalman filter with unknown input (GILS-EKF-UI) procedure, developed earlier by the research team. It is demonstrated that the proposed UKF-based procedures are superior to the EKF-based procedures for SHA.

Cette thèse étudie le problème d'identification de la topologie d'un réseau de systèmes complexes dynamiques, dont les sous-systèmes sont décrits par des équations différentielles ordinaires (EDO) et/ou par des équations différentielles à retard (EDR). La première partie de ce travail porte sur l’identification des paramètres du réseau de systèmes linéaires. Ainsi, différentes classes de systèmes linéaires ont été traitées, à savoir les systèmes sans retard, les systèmes à retard commensurable et les systèmes à entrées inconnues. Un observateur impulsif est proposé afin d'identifier à la fois les états et les paramètres inconnus de la classe de système dynamique considérée en temps fini. Afin de garantir l'existence de l'observateur impulsif proposé, des conditions suffisantes sont déduites. Des exemples illustratifs sont donnés afin de montrer l'efficacité de l'observateur en temps fini proposé.La deuxième partie de ce travail traite le problème de l'identification de la topologie d'un réseau de systèmes dynamiques non linéaires. Dans nos considérations, les coefficients interconnexions de la topologie du réseau sont considérés comme des paramètres constants. Par conséquent, l'identification de la topologie est équivalente à l'identification des paramètres inconnus. Tout d’abord, nous avons déduit des conditions suffisantes sur l’identifiabilité des paramètres, puis nous avons proposé un différenciateur uniforme avec convergence en temps fini pour estimer les paramètres inconnus / This thesis investigates the topology identification problem for network of dynamical complex systems, whose subsystems are described by ordinary differential equations (ODE) and/or delay differential equations (DDE). The first part of this work focuses on the parameters identification of the network of linear systems. Thus, different classes of linear systems have been treated namely systems without delay, systems with commensurable delay and systems with unknown inputs. An impulsive observer is proposed in order to identify both the states and the unknown parameters of the considered class of dynamic system in finite time. In order to guarantee the existence of the proposed impulsive observer, sufficient conditions are deduced. An illustrative example is given in order to show the efficiency of the proposed finite-time observer.The second part of this work treats the topology identification of the network of nonlinear dynamic systems. In our considerations, the topology connections are represented as constant parameters, therefore the topology identification is equivalent to identify the unknown parameters. A sufficient condition on parameter identifiability is firstly deduced, and then a uniform differentiator with finite-time convergence is proposed to estimate the unknown parameters

The research in this thesis is undertaken by observing that modern systems are becoming more and more complex and safety-critical due to the increasing requirements on system smartness and autonomy, and as a result health monitoring system needs to be developed to meet the requirements on system safety and reliability. The state-of-the-art approaches to monitoring system status are model based Fault Diagnosis (FD) systems, which can fuse the advantages of system physical modelling and sensors' characteristics. A number of model based FD approaches have been proposed. The conventional residual based approaches by monitoring system output estimation errors, however, may have certain limitations such as complex diagnosis logic for fault isolation, less sensitiveness to system faults and high computation load. More importantly, little attention has been paid to the problem of fault diagnosis system verification which answers the question that under what condition (i.e., level of uncertainties) a fault diagnosis system is valid. To this end, this thesis investigates the design and verification of fault diagnosis algorithms. It first highlights the differences between two popular FD approaches (i.e., residual based and fault estimation based) through a case study. On this basis, a set of uncertainty estimation algorithms are proposed to generate fault estimates according to different specifications after interpreting the FD problem as an uncertainty estimation problem. Then FD algorithm verification and threshold selection are investigated considering that there are always some mismatches between the real plant and the mathematical model used for FD observer design. Reachability analysis is drawn to evaluate the effect of uncertainties and faults such that it can be quantitatively verified under what condition a FD algorithm is valid. First the proposed fault estimation algorithms in this thesis, on the one hand, extend the existing approaches by pooling the available prior information such that performance can be enhanced, and on the other hand relax the existence condition and reduce the computation load by exploiting the reduced order observer structure. Second, the proposed framework for fault diagnosis system verification bridges the gap between academia and industry since on the one hand a given FD algorithm can be verified under what condition it is effective, and on the other hand different FD algorithms can be compared and selected for different application scenarios. It should be highlighted that although the algorithm design and verification are for fault diagnosis systems, they can also be applied for other systems such as disturbance rejection control system among many others.

La commande de systèmes physiques s’avère être une tâche difficile en général. En fonction du modèle choisi, les outils mathématiques pour l’analyse et la conception de lois de commande peuvent changés. Pour les systèmes décrits par une représentation entrée-sortie, type transfert, ou par une équation de type état, les principales informations exploitées lors de la phase d’analyse concerne la structure interne du modèle (structure finie) et la structure externe (structure à l’infini) qui permettent avant la phase de synthèse de connaître, sur le modèle en boucle ouverte, les propriétés des lois de commande envisagées ainsi que les propriétés du système piloté (stabilité…).Le travail porte principalement sur l’étude des zéros invariants des systèmes physiques représentés par bond graph, en particulier dans un contexte de modèle type LTV. L’approche algébrique est essentielle dans ce contexte car même si les aspects graphiques restent très proches du cas linéaire classique, l’extension aux modèles LTV reste très complexe d’un point de vue mathématique, en particulier pour le calcul de racines de polynômes. De nouvelles techniques d’analyse des zéros invariants utilisant conjointement l’approche bond graph (exploitation de la causalité) et l’approche algébriques ont permis de mettre en perspective certains modules associés à ces zéros invariants et de clarifier le problème d’annulation des grandeurs de sortie. L’application aux problèmes d’observateurs à entrées inconnues a permis d’illustrer nos propos sur des exemples physiques, avec certaines extensions, problèmes pour lesquels les zéros invariants apparaissent aussi comme éléments essentiels / The control synthesis of physical systems is a complex task because it requires the knowledge of a "good model" and according to the choice of a model some specific tools must be developed. These tools, mainly developed from a mathematical and theoretical point of view, must be used from the analysis step (analysis of model properties) to the control synthesis step. It is well-known that in many approaches, the properties of the controlled systems can be analyzed from the initial model. If the system is described with an input-output representation or with a state space representation, two kinds of information are often pointed out: the external structure (infinite structure) and the internal structure (finite structure). The first one is often related to the existence of some control strategies (input-output decoupling, disturbance decoupling...) and the second one gives some focus on the stability property of the controlled system.In this report, the focus has been on the study of invariant zeros of bond graph models in the context of LTV models. The algebraic approach was essential because, even if the problem is already solved for LTI bond graph models, the extension to LTV models is not so easy. The simultaneous use of algebraic and graphical approaches has been proven to be effective and convenient to solve this problem. First, some tools from the algebraic approach have been recalled in chapter one and results for the study of invariant zeros of LTI bond graph models recalled in chapter two. Some new developments are proposed in chapter three and some applications for the unknown input observer problem with some physical applications conclude this work

Au cours de la dernière décennie, l’industrie des véhicules aériens sans pilote (UAV) a connu une croissance et une diversification immenses. De nos jours, nous trouvons des applications basées sur les drones dans un large éventail d’industries, telles que les infrastructures, l’agriculture, les transports, etc. Ce phénomène a suscité un intérêt croissant dans le domaine de la manipulation aérienne. La mise en œuvre de manipulateurs aériens dans l'industrie des UAV pourrait générer une augmentation significative du nombre d'applications possibles. Cependant, la restriction de la charge utile disponible est l’un des principaux inconvénients de cette approche. L'impossibilité d'équiper les drones de bras robotiques industriels puissants et habiles a suscité l'intérêt pour le développement de manipulateurs légers adaptés à ces applications. Dans le but de fournir une solution légère alternative aux manipulateurs aériens, cette thèse propose un bras robotique léger actionné par des fils en alliage à mémoire de forme (SMA). Bien que les fils SMA représentent une excellente alternative aux actionneurs conventionnels pour les applications légères, ils impliquent également une dynamique hautement non linéaire, ce qui les rend difficiles à contrôler. Cherchant à présenter une solution pour la tâche difficile de contrôler les fils SMA, ce travail étudie les conséquences et les avantages de la mise en œuvre des techniques de commande par retour d’état. L'objectif final de cette étude est la mise en œuvre expérimentale d'un contrôle à rétroaction d'état pour la régulation de la position du bras robotique léger proposé. Tout d'abord, un modèle mathématique basé sur un modèle physique du comportement des câbles SMA est développé et validé expérimentalement. Ce modèle décrit la dynamique du bras robotique léger proposé du point de vue de la mécatronique. Le bras robotique proposé est testé avec trois contrôleurs de retour de sortie pour le contrôle de position angulaire, à savoir un PID, un mode coulissant et une commande adaptative. Les contrôleurs sont testés dans une simulation MATLAB, puis mis en œuvre et testés expérimentalement selon différents scénarios. Ensuite, afin de réaliser la mise en œuvre expérimentale d’une technique de commande par retour d’état, un observateur d’état, à entrée inconnue, est développé. Premièrement, un modèle observable sans commutation avec une entrée inconnue est dérivé du modèle présenté précédemment. Ce modèle prend comme entrée inconnue le taux de fraction de martensite du modèle d'origine, ce qui permet d'éliminer les termes de commutation dans le modèle. Ensuite, un observateur, à entrées inconnues, basé sur le filtre de Kalman étendu et sur l’observateur à mode glissant est développé. Cet observateur permet l’estimation simultanée de l’état et des entrées inconnues. Les conditions suffisantes de convergence et de stabilité sont établies. L'observateur est testé dans une simulation MATLAB et validé expérimentalement dans différents scénarios. Enfin, une technique de commande par retour d’état est testée en simulation et implémentée de manière expérimentale pour le contrôle de position angulaire du bras robotique léger proposé. Elle est basée sur la résolution d’une équation de Riccati (SDRE). En conclusion, une analyse comparative quantitative et qualitative entre une approche de commande par retour de sortie et la une de commande par retour d’état mis en œuvre est effectuée selon plusieurs scénarios, y compris la régulation de position, le suivi de position et le suivi de charges utiles changeantes. / In the last decade, the industry of Unmanned Aerial Vehicles (UAV) has gone through immense growth and diversification. Nowadays, we find drone based applications in a wide range of industries, such as infrastructure, agriculture, transport, among others. This phenomenon has generated an increasing interest in the field of aerial manipulation. The implementation of aerial manipulators in the UAV industry could generate a significant increase in possible applications. However, the restriction on available payload is one of the main setbacks of this approach. The impossibility to equip UAVs with heavy dexterous industrial robotic arms has driven the interest in the development of lightweight manipulators suitable for these applications. In the pursuit of providing an alternative lightweight solution for the aerial manipulators, this thesis proposes a lightweight robotic arm actuated by Shape Memory Alloy (SMA) wires. Although SMA wires represent a great alternative to conventional actuators for lightweight applications, they also imply highly nonlinear dynamics, which makes them difficult to control. Seeking to present a solution for the challenging task of controlling SMA wires, this work investigates the implications and advantages of the implementation of state feedback control techniques. The final aim of this study is the experimental implementation of a state feedback control for position regulation of the proposed lightweight robotic arm. Firstly, a mathematical model based on a constitutive model of the SMA wire is developed and experimentally validated. This model describes the dynamics of the proposed lightweight robotic arm from a mechatronics perspective. The proposed robotic arm is tested with three output feedback controllers for angular position control, namely a PID, a Sliding Mode and an Adaptive Controller. The controllers are tested in a MATLAB simulation and finally implemented and experimentally tested in various different scenarios. Following, in order to perform the experimental implementation of a state feedback control technique, a state and unknown input observer is developed. First, a non-switching observable model with unknown input of the proposed robotic arm is derived from the model previously presented. This model takes the martensite fraction rate of the original model as an unknown input, making it possible to eliminate the switching terms in the model. Then, a state and unknown input observer is proposed. This observer is based on the Extended Kalman Filter (EKF) for state estimation and sliding mode approach for unknown input estimation. Sufficient conditions for stability and convergence are established. The observer is tested in a MATLAB simulation and experimentally validated in various different scenarios. Finally, a state feedback control technique is tested in simulation and experimentally implemented for angular position control of the proposed lightweight robotic arm. Specifically, continuous and discrete-time State-Dependent Riccati Equation (SDRE) control laws are derived and implemented. To conclude, a quantitative and qualitative comparative analysis between an output feedback control approach and the implemented state feedback control is carried out under multiple scenarios, including position regulation, position tracking and tracking with changing payloads.