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Thesis (Ph. D.)--Lehigh University, 2002. / Includes vita. Includes bibliographical references (leaves 203-206).

Observers are used in the monitoring and control of dynamical systems to deduce the values of unmeasured states. Designing an observer requires having an accurate model of the plant — if the model parameters are characterized imprecisely, the observer may not provide reliable estimates. An interval observer, which comprises an upper and lower observer, bounds the plant's states from above and below, given the range of values of the imprecisely characterized parameters, i.e., it defines an interval in which the plant's states must lie at any given instant. We propose a linear programming-based method of interval observer design for two cases: 1) only the initial conditions of the plant are uncertain; 2) the dynamical parameters are also uncertain. In the former, we optimize the transient performance of the interval observers, in the sense that the volume enclosed by the interval is minimized. In the latter, we optimize the steady state performance of the interval observers, in the sense that the norm of the width of the interval is minimized at steady state. Interval observers are typically designed to characterize the widest interval that bounds the states. This thesis proposes an interval observer design method that utilizes additional, but still-incomplete information, that enables the designer to identify tighter bounds on the uncertain parameters under certain operating conditions. The number of bounds that can be refined defines a class of systems. The definition of this class is independent of the specific parameters whose bounds are refined. Applying robust optimization techniques, under a cardinality constrained model of uncertainty, we design a single observer for an entire class of systems. These observers guarantee a minimum level of performance with respect to the aforementioned metrics, as we optimize the worst-case performance over a given class of systems. The robust formulation allows the designer to tune the level of uncertainty in the model. If many of the uncertain parameter bounds can be refined, the nominal performance of the observer can be improved, however, if few or none of the parameter bounds can be refined, the nominal performance of the observer can be designed to be more conservative.

Observers are used in the monitoring and control of dynamical systems to deduce the values of unmeasured states. Designing an observer requires having an accurate model of the plant — if the model parameters are characterized imprecisely, the observer may not provide reliable estimates. An interval observer, which comprises an upper and lower observer, bounds the plant's states from above and below, given the range of values of the imprecisely characterized parameters, i.e., it defines an interval in which the plant's states must lie at any given instant. We propose a linear programming-based method of interval observer design for two cases: 1) only the initial conditions of the plant are uncertain; 2) the dynamical parameters are also uncertain. In the former, we optimize the transient performance of the interval observers, in the sense that the volume enclosed by the interval is minimized. In the latter, we optimize the steady state performance of the interval observers, in the sense that the norm of the width of the interval is minimized at steady state. Interval observers are typically designed to characterize the widest interval that bounds the states. This thesis proposes an interval observer design method that utilizes additional, but still-incomplete information, that enables the designer to identify tighter bounds on the uncertain parameters under certain operating conditions. The number of bounds that can be refined defines a class of systems. The definition of this class is independent of the specific parameters whose bounds are refined. Applying robust optimization techniques, under a cardinality constrained model of uncertainty, we design a single observer for an entire class of systems. These observers guarantee a minimum level of performance with respect to the aforementioned metrics, as we optimize the worst-case performance over a given class of systems. The robust formulation allows the designer to tune the level of uncertainty in the model. If many of the uncertain parameter bounds can be refined, the nominal performance of the observer can be improved, however, if few or none of the parameter bounds can be refined, the nominal performance of the observer can be designed to be more conservative.

Dans ce travail de thèse, nous développons des méthodes de synchronisation des systèmes chaotiques pour les applications de transmission d'informations. La première méthode de synchronisation que nous proposons est basée sur les observateurs adaptatifs à entrées inconnues pour une classe des systèmes chaotiques présentant des incertitudes paramétriques et des perturbations dans leurs dynamiques et du bruit dans les signaux de sortie (bruit dans le canal de communication). La méthode développée repose sur les techniques adaptatives pour la compensation des non-linéarités et des incertitudes paramétriques et pour la restauration des messages transmis. Elle se base également sur les méthodes de synthèse d'observateurs à entrées inconnues pour supprimer l'influence des perturbations et du bruit. Ensuite, nous développons une deuxième méthode de synchronisation utilisant un observateur adaptatif à ``modes glissants" pour une classe des systèmes chaotiques présentant des entrées inconnues et dont les signaux de sortie sont bruités. La synthèse de l'observateur s'appuie sur la théorie des modes glissants, les techniques de synthèse d'observateurs singuliers et les techniques adaptatives dans le but d'estimer conjointement l'état et les entrées inconnues malgré la présence du bruit dans les équations de sortie. Cette approche de synchronisation est ensuite employée dans un nouveau schéma de communication chaotique sécurisée dont l'objectif est d'augmenter le nombre et l'amplitude des messages transmis, améliorer le niveau de sécurité ainsi que la robustesse aux bruits présents dans le canal de communication. En outre, le scénario de présence des retards de transmission est étudié en élaborant une troisième approche de synchronisation à base d'observateurs adaptatifs pour une classe des systèmes chaotiques de Lur'e avec des non-linéarités à pente restreinte et des signaux de sortie retardés. En se basant sur la théorie de Lyapunov-Krasovskii et en utilisant une hypothèse d'excitation persistante, l'observateur adaptatif proposé garantit la synchronisation maitre-esclave et la restauration des informations transmises malgré l'existence des retards de transmission. Les résultats théoriques obtenus dans ce travail de thèse sont vérifiés à travers des applications de transmission d'informations utilisant différents modèles des systèmes chaotiques tout en étudiant les différents scénarios et cas de figure pouvant se présenter en pratique et en analysant les aspects de sécurité de ces systèmes. / In this thesis, we develop synchronization methods of chaotic systems for information transmission applications. The first proposed method is based on adaptive unknown input observers for a class of chaotic systems subject to parametric uncertainties and perturbations in their dynamics and noise in outputs signals (Channel communication noise). The developed method is based on adaptive techniques to compensate nonlinearities to compensate nonlinearities and parametric uncertainties and to reconstruct the transmitted messages. Furthermore, this approach is based on unknown input observers design to reject the influence of perturbations and noise. Then, we develop a second synchronization method using an adaptive ``sliding mode” observer for a class of chaotic systems subject to unknown inputs and such that the output equations are subject to noise. The observer design is based on sliding modes theory, descriptor observers design and adaptive control in order to join state and unknown input estimation despite the presence of noise in output equations. The latter synchronization approach is then exploited in a new secured communication scheme where the objective is to increase the number and amplitude of the transmitted messages, improve the level of security and the robustness to noise present in the communication channel. Moreover, the case of presence of transmission time-delays was investigated and a synchronization approach based on adaptive observers for a class of Lur’e systems with slope restricted nonlinearities and delayed outputs. Based on the Lyapunov-Krasovskii theory and using a persistency of excitation property, the proposed adaptive observer ensures master-slave synchronization and the reconstruction of the transmitted messages despite the existence of transmission time-delays. The obtained theoretical results in this thesis are verified through transmission information applications using different models of chaotic systems in different scenarios and case-studies which may occur in practice. Cryptanalysis and security aspects of the proposed communication systems are also investigated.

Teleoperation systems have been used in the operating rooms for more than a decade. However, the lack of force feedback in commercially available systems still raises safety issues and forbids surgical gestures like palpation. Although force feedback has already been implemented in experimental setups, a systematic methodology is still lacking to design the control laws. The approach developed in this thesis is a contribution towards such a systematic methodology: it combines the use of disturbance observers with the use of a structured fixed-order controller. This approach is validated by experiments performed on a one degree of freedom teleoperation system. A physical model of this system is proposed and validated experimentally. Disturbance observers allow to compensate friction, which is responsible for performance degradation in teleoperation. Contrary to alternative approaches,they are based on a model of the frictionless mechanical system. This allows to compensate friction with a time varying behavior, which occurs in laparoscopy. Parametric uncertainties in this model may lead to an unstable closed-loop. A kind of "separation principle" is provided to decouple the design of the closed-loop system from the design of the observer. It relies on a modified problem statement and on the use of available robust design and analysis tools. A new metric is proposed to evaluate the performance of friction compensation systems experimentally. This metric evaluates the ability of a compensation system to linearize a motion system, irrespective of the task and as a function of frequency. The observer-based friction compensation is evaluated with respect to this new metric and to a task-based metric. It correctly attenuates the friction in the bandwidth of interest and significantly improves position and force tracking during a palpation task. Structured fixed-order controllers are optimized numerically to achieve robust closed-loop performance despite modeling uncertainty. The structure is chosen among classical teleoperation structures. An efficient algorithm is selected and implemented to design such a controller, which is evaluated for a palpation task. It is compared to a full-order unstructured controller, representative of the design approach that has been used in the teleoperation literature up to now. The comparison highlights the advantages of our new approach: order-reduction steps and counter-intuitive behaviors are avoided. A structured fixed-order controller combined with a disturbance observer is implemented during a needle insertion experiment and allowed to obtain excellent performance.

This thesis concerns the identification of dynamic models in systems biology. and is structured into two parts. Both parts concern building dynamic models from observed data, but are quite different in perspective, rationale and mathematics. The first part considers the development of novel identification techniques that are particularly tailored to (molecular) biology and considers two approaches. The first approach reformulates the parameter estimation problem as a feasibility problem. This reformulation allows the invalidation of models by analysing entire parameter regions. The second approach utilises nonlinear observers and a transformation of the model equations into parameter free coordinates. The parameter free coordinates allow the design of a globally convergent observer, which in turn estimates the parameter values, and further, allows to identify modelling errors or unknown inputs/influences. Both approaches are bottom up approaches that require a mechanistic understanding of the underlying processes (in terms of a biochemical reaction network) leading to complex nonlinear models. The second part is an example of what can be done with classical, well developed tools from systems identification when applied to hitherto unattended problems.In particular, part two of my thesis develops a modelling framework for rat movements in an experimental setup that it widely used to study learning and memory.The approach is a top down approach that is data driven resulting in simple linear models.

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Based on the Lyapunov stability theorem, an adaptive variable structure observer and a controller are proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems with unmeasurable states to solve regulation and tracking problems. In order to estimate the unmeasurable states, a design methodology of variable structure observers is presented first. Then the controller is designed so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. Some adaptive mechanisms are embedded in the sliding surface function and sliding mode controllers, so that not only the mismatched perturbations are suppressed effectively during the sliding mode, but also the information of upper bounds of some perturbations are not required. When the controlled system is the sliding mode, the stability or asymptotical stability is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed design technique.

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