When designing or reviewing control systems, it is important to understand the limitations of the system's design. Many systems today are designed using numerical methods. Although the numerical model may be controllable, stabilizable, or stable, small perturbations of the system parameters can result in the loss of these properties. In this thesis, we investigate these issues for finite element approximations of a thermal convection loop. / Master of Science

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O trabalho apresenta inicialmente os conceitos clássicos de rolamento (sem escorregamento e sem pivotamento) de uma superfície sobre outra usando os triedros de Darboux das duas superfícies ao longo das respectivas curvas de contato. Mostra, ainda, a equivalência desses conceitos com outras definições. A seguir, estuda-se a controlabilidade no problema do rolamento de uma esfera sobre uma superfície S de revolução, tanto no caso de rolar sem escorregar como no caso de não escorregar e não pivotar; a controlabilidade visa determinar a atingibilidade entre dois 'estados' da esfera (posição em S e orientação), isto é, de elementos do espaço das configurações S×SO(3). Na seqüência, estabelecem-se condições nos controles para que os rolamentos sem escorregamento e sem pivotamento ocorram sobre geodésicas de S e obtém-se, também, a controlabilidade nesta situação. Finalmente, verifica-se que, quando S é um plano, 3 ou 4 rolamentos retilíneos, sem escorregamento e sem pivotamento, são suficientes para garantir a atingibilidade entre dois “estados" da esfera. / This work starts by presenting the classical concepts of rolling (without slipping and without slipping or twisting) of a surface over another one, using the Darboux referential frames of the two surfaces along their contact curves. It shows the equivalence between these concepts with other definitions. In the sequel one studies the controllability in the rolling problem of a ball over a surface of revolution S, including both: the non slipping and the non slipping or twisting cases; controllability aims to determine the reachability between two 'states'of the ball (position on S and orientation), that is, two elements of the configuration space S × SO(3). It follows by establishing conditions on controls in order that the rollings occur along geodesics of S and by studying the controllability in this situation. Finally, it is shown that if S is the plane, 3 or 4 retilinear moves without slipping or twisting are enough to guarantee reachability between two states of the ball.

Vehicle behaviour near the limit of adhesion is studied using linear optimal . control techniques and relatively simple vehicle models. Both time-invariant and time-varying approaches are used. Controllability is applied as a post-processing tool to analyse the resultant vehicle behaviour. First, a 4WS controller is developed using a linear time-invariant method, with a reference model control structure. Two handling objectives are defined, which are thought to provide predictable dynamics. Advantages of using a reference model control are clearly shown. With a developed control structure, it is shown that the prescribed target dynamics is achieved, provided tyre forces are available. It is also found that the controller is robust to small changes in the various vehicle parameter values. As a next step, time-varying modelling approach was used in order to better represent the vehicle operating conditions through the various dynamic range, including the limit of adhesion. An iterative vehicle path optimisation problem is formulated using a linear time-varying control approach. The validity of the optimisation method is studied against the steady-state simulation result at the limit of adhesion. It is shown that the method is capable of finding a trajectory in the vicinity of the friction limit, where the front tyres are used fully whilst retaining some margin at the rears. However, a couple of Issues are discovered. First, due to the quadratic nature of the road geometry cost function, the trajectory could get locked if the vehicle runs very close to the edge of the road. Hence, the . optimisation needs to be formulated such that the level of "optimality" on the trajectory remains consistent throughout the manoeuvre at each iteration. Secondly, it is found that inappropriate control demands are produced if the system matrix becomes poorly conditioned near the limit. This results in optimisation failure. In order to understand the mechanism of this failure, controllability of linear timevarying system was analysed and its properties were discussed in detail. First, the calculation methods of the controllability gramian matrix are investigated and some practical limitations are found. The gramian matrix is then used to define an open loop control sequence. It is found that the damping of the system has a significant influence on the control strategy. Subsequently, "the moving controllability window of a fixed time period" is found to provide the most relevant information of changing dynamics through the time. The study showed that the failure of the optimisation in the vicinity of the friction limit was indeed due to lack of controllability and the optimisation method itself was functioning correctly. The vehicle path optimisation problem is then extended to include longitudinal dynamics, enabling simulation of more general manoeuvres. The single corner simulation showed that the optimisation converges to an "out-in-out" path, with iterative solution improving continuously in a first order manner. Simulations with various controller settings showed that the strategy is reasonably robust provided that the changes in parameter settings are kept within a reasonable magnitude. It is also confirmed that the optimisation is able to drive a vehicle close to the limit under different types of operations required, i.e. braking, cornering and acceleration. The study was then performed with slightly more complex road geometry in order to investigate if the· optimisation is capable of prioritising certain· part of the manoeuvre in order to achieve better overall result. Unfortunately, this problem could not be solved successfully. The optimisation concentrated on the latter part of the manoeuvre as it had higher sensitivity to the final cost. This resulted in clearly sub-optimal overall performance. Finally, relatively simple study is conducted to investigate the correlation between various vehicle settings and optimisation results. Using the path optimisation problem formulation, iris found that the more oversteer vehicles are able to achieve better· result with more margin left in rear tyre force capacity. The handling objective functions used for the 4 WS controller is also calculated for the resultant trajectories. It is found that the neutral steer cost had a strong correlation, whereas the linearity cost showed no noticeable correlation. The controllability analysis was applied on the various vehicle settings using step steer simulation. It showed that more understeering vehicle retains higher controllability throughout the dynamics range. It is also found that higher inertia gives better controllability near the limit, however, it gives less controllability at more moderate operating conditions.

Cette thèse est consacrée à la contrôlabilité et à l’observabilité de l’équation d’évolution non autonome. Dans la première partie, nous donnons un aperçu de la théorie du contrôle ainsi que quelques résultats classiques sur le contrôle des systèmes autonomes et non autonomes. En fait, nous rappellerons les techniques de la théorie des semi-groupes, théorie de l’évolution familiale, théorie de la dualité et de l’opérateur. Dans la deuxième partie, nous sommes intéressés à étudier le problème de contrôle pour les systèmes EDP définis sur des domaines dépendant du temps. Nous développons de nouvelles techniques pour obtenir les résultats sur l’observabilité exacte des équations de l’onde et de Schrödinger 1D, puis par dualité nous établissons la contrôlabilité exacte du système adjoint. Le dernier résultat est une généralisation des tests de Hautus pour l’observabilité du système d’évolution non autonome. Notre méthode peut s’appliquer aux équations de Schrödinger et à l’équation d’onde avec des potentiels dépendant du temps. / This thesis is devoted to the controllability and observability of nonautonomous evolution equation. In the first part, we give an overview on control theory as well as some classical results on control of both autonomous and nonautonomous systems. In fact, we will recall the technique in semigroup theory, evolution familys theory, duality theory and operator theory. In the second part, we are interested to investigate the control problem for PDEs systems defined on time-dependent domains. We develope some new techniques to obtain the results on exact observability for one dimensional wave and Schrödinger equations, then by duality we establish exact controllability of adjoint system. The last result is a generalization of Hautus tests for observability of non- autonomous evolution system.Our method can apply for Schrodinger equations with time dependent potentials and to a damped wave-equation with time-dependent damping.

Dans cette thèse, on étudie la contrôlabilité et la stabilisation de certaines équations aux dérivées partielles . On s'intéresse d'abord au problème du contrôle de l'équation d'Euler 3D incompressible par une force extérieure de dimension finie. Nous montrons que pour un choix approprié de l'espace de contrôle, la vitesse et la pression du fluide sont exactement contrôlables en projections. De plus, la vitesse est approximativement contrôlable. Nous montrons aussi que le système en question n'est pas exactement contrôlable par une force extérieure de dimension finie.On étudie aussi la contrôlabilité de l'équation d'Euler 3D compressible. Le contrôle est une force extérieure de dimension finie agissant uniquement sur l'équation de la vitesse. Nous montrons que la vitesse et la densité du fluide sont simultanément contrôlables. En particulier, le système est approximativement contrôlable et exactement contrôlable en projections. Dans la dernière partie, on étudie la stabilisation de l'équation d'Euler dans un cylindre infini.Nous montrons que pour toute solution stationnaire (c,0) du système d'Euler il existe un contrôle supporté dans une partie de la frontière du cylindre qui stabilise le système à (c,0). / In this thesis, we study the controllability and stabilization of certain partial differential equations.We consider first the problem of control of the 3D incompressible Euler equationby an external force of finite dimension. We show that for an appropriate choice of control space, the velocity and the pressure of the fluid are exactly controllable in projections.Moreover, the velocity is approximately controllable. We also show that the system in question is not exactly controllable by a finite-dimensional external force.We also study the controllability of the 3D compressible Euler equation. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are simultaneously controllable. In particular, the system is approximately controllable and exactly controllable in projections.The last section of the thesis is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c,0) of the Euler system there is a control which is supported in a given bounded part of the boundary of the strip and stabilizes the system to (c,0).

O trabalho apresenta inicialmente os conceitos clássicos de rolamento (sem escorregamento e sem pivotamento) de uma superfície sobre outra usando os triedros de Darboux das duas superfícies ao longo das respectivas curvas de contato. Mostra, ainda, a equivalência desses conceitos com outras definições. A seguir, estuda-se a controlabilidade no problema do rolamento de uma esfera sobre uma superfície S de revolução, tanto no caso de rolar sem escorregar como no caso de não escorregar e não pivotar; a controlabilidade visa determinar a atingibilidade entre dois 'estados' da esfera (posição em S e orientação), isto é, de elementos do espaço das configurações S×SO(3). Na seqüência, estabelecem-se condições nos controles para que os rolamentos sem escorregamento e sem pivotamento ocorram sobre geodésicas de S e obtém-se, também, a controlabilidade nesta situação. Finalmente, verifica-se que, quando S é um plano, 3 ou 4 rolamentos retilíneos, sem escorregamento e sem pivotamento, são suficientes para garantir a atingibilidade entre dois “estados” da esfera. / This work starts by presenting the classical concepts of rolling (without slipping and without slipping or twisting) of a surface over another one, using the Darboux referential frames of the two surfaces along their contact curves. It shows the equivalence between these concepts with other definitions. In the sequel one studies the controllability in the rolling problem of a ball over a surface of revolution S, including both: the non slipping and the non slipping or twisting cases; controllability aims to determine the reachability between two 'states'of the ball (position on S and orientation), that is, two elements of the configuration space S × SO(3). It follows by establishing conditions on controls in order that the rollings occur along geodesics of S and by studying the controllability in this situation. Finally, it is shown that if S is the plane, 3 or 4 retilinear moves without slipping or twisting are enough to guarantee reachability between two states of the ball.

Semiconductor supply chain is increasingly getting exposed to Reverse Engineering (RE) of Intellectual Property (IP). Camouflaging of gates in integrated circuits are typically employed to hide the gate functionality to prevent reverse engineering. The functionalities of these gates cannot be found by De-layering as they don’t leave any layout clues. Adversaries perform reverse engineering by replacing the camouflaged gate with the known gate and by developing custom software to determine test patterns. These test patterns are used to analyze the outputs and to conclude the functionality of the camouflaged gate. In this thesis, we show that reverse engineering of camouflaged design can be performed by exploiting the test features of commercial/publicly available Automatic Test Pattern Generation (ATPG) tools. We also propose controllability/observability and Hamming Distance sensitivity based metric to select target gates for camouflaging. Simulations on ISCAS85 benchmarks shows that the proposed techniques can increase the reverse engineering effort significantly by camouflaging small fraction of gates.

The diploma thesis deals with evaluation and suggestion of changes for the conceptual design of an airplane TL4000 in terms of stability and controllability. In the first part there are determined stability and controllability derivativations of the aircraft. Thereafter are estimated aircraft weight, moment of inertia and necessary geometric characteristics. In the second part there are calculated stability criteria for a sample case. In the third part, on the basis of this calculation, a program is created. This program combines the advantages of MS Excel, Matlab and Matlab Simulink. By means of this program criteria of stability and controllability were calculated parametrically for different regimes of flight, identified critical cases and compared with the requirements of CS-23rd. Based on this evaluation were recommanded modifications of the conceptual design TL4000.

This dissertation examines whether the magnitude of the outcome effect is impacted by the type of performance evaluation system (subjective versus formula-based). The outcome effect is a phenomenon that occurs when an evaluator overemphasizes the outcome of a decision and ignores essential information that is available to the evaluator (e.g., market information, information about the decision-making process). This outcome focus leads to a more positive (negative) performance evaluation when the outcome exceeds (fails to meet) expectations. Prior studies have not examined whether the type of evaluation system (formula-based versus subjective) has an impact on the magnitude of the outcome effect. In a formula-based evaluation system, outcome measures are pre-weighted and an overall variance measure is easily calculated. Conversely, there are no predefined weights or overall variance measures in a subjective system. Instead, evaluators weight the importance of outcome information themselves. For this dissertation, I conducted an experiment in which 99 business professionals enrolled in a MBA program evaluated the performance of a retail store manager. Their evaluation was based on information that they received about the manager's decision, along with situational factors that may have impacted the decision outcome. The results demonstrate that although the magnitude of the outcome effect was larger when a formula-based system was employed relative to a subjective system, this difference was not statistically significant. Nonetheless, this study provides initial evidence that managers using formula-based evaluation systems should be particularly aware of the outcome effect when conducting performance appraisals. In addition, this study documents the perceived controllability of four financial and four non-financial measures that are commonly employed to evaluate performance in the retail industry. As hypothesized, the non-financial measures were perceived to be more controllable than the financial measures. This suggests that non-financial measures should be included in the mix of performance measures used in a performance appraisal system. / Ph. D.