L’objectif de ce manuscrit est de fournir une technique de commande tolérante aux défauts basée sur la platitude différentielle. Pour ce type de systèmes, il est possible de trouver un ensemble de variables, nommées sorties plates, tel que, les états et les entrées de commande du système puissent s’exprimer en fonction de ces sorties et d’un nombre fini de ses dérivées temporelles. Le bloc de détection et d’isolation doit assurer la détection du défaut le plus rapidement possible. Cette action est effectuée en exploitant la propriété de non-unicité des sorties plates. En effet, si un deuxième jeu de sorties plates peux être trouvé et si ce deuxième jeu n’est couplé avec le premier que par une équation différentielle, le nombre des résidus permettant la détection de défauts pourra être augmenté. La condition pour cela est que les deux jeux soient différentiellement couplés ce qui signifie qu’il existe une équation qui contienne des dérivées temporelles et qui couple un élément du premier jeu avec un élément du deuxième jeu de sorties plates. En conséquence le nombre de résidus disponibles pour la détection est supérieur au nombre que l’on aurait si on avait seulement un jeu des sorties plates.En ce qui concerne la reconfiguration, si le système plat satisfait les propriétés énumérées ci-dessus, nous obtiendrons autant de valeurs des états et des entrées que le nombre de jeux de sorties plates trouvés. En effet chaque entrée de commande et chaque état du système peuvent être recalculés en fonction des sorties plates. L’approche proposée fournit de cette manière un résidu prenant en compte une mesure calculée avec le vecteur plat contenant le défaut et une autre avec le vecteur plat libre de défaut. Les signaux redondants libres de défauts seront ainsi utilisés comme références du contrôleur de manière à ce que les effets du défaut soient masqués et ne rentrent pas la boucle de commande. Ceci sera utile pour fournir une stratégie de commande entièrement basée sur les systèmes plats.Les travaux présentés dans ce mémoire sont donnés sous l’hypothèse suivante: Les sorties plates sont fonctions de l’état du système, néanmoins dans ce manuscrit elles seront limitées à être directement une partie de l’état du système ou une combinaison linéaire d’entre eux. La boucle de commande est fermée avec un correcteur par retour d’état.Enfin pour les travaux réalisés en fin de manuscrit les sorties plates doivent pouvoir être mesurées ou reconstruites.Les défauts affectant les actionneurs sont considérés rejetés par le contrôleur, par conséquent la reconfiguration est seulement effectuée après la détection d’un défaut capteur.La faisabilité de l’approche proposée est analysée sur deux systèmes non linéaires, un drone quadrirotor et un système de trois cuves. / The objective of this Ph.D. work is to provide a flatness based active fault-tolerant control technique. For such systems, it is possible to find a set of variables, named flat outputs, such that states and control inputs can be expressed as functions of flat outputs and their time derivatives. The fault detection and isolation block has to provide a fast and accurate fault isolation. This action is carried out by exploiting the non-uniqueness property of the flat outputs. In fact, if a second set of flat outputs which are coupled by a differential equation of the first is calculated, bthe number of residues augments. Differentially coupled means that it exists an equation with time derivatives inside, that couple one element of the first set with one of the second. As a consequence of augmenting the number of residual signal more faults than in the one set case may be isolated.Regarding reconfiguration, if the flat system complies with the properties listed above, we will obtain versions of states and control inputs as much of flat output vectors, are found, because each control input and state is a function of the flat output. The proposed approach provides in this manner one measure related to a faulty flat output vector and one or more computed by using an unfaulty one. The redundant state signals could be used as reference of the controller in order to hide the fault effects. This will be helpful to provide an entirely flatness based fault-tolerant control strategy.The works presented in this manuscript are under the following hypothesis: The flat outputs are functions of the state of the system, however in this work the flat outputs are constrained to be states of the system or a linear combination of them.The control loop is closed with a state feedback controller.For purposes of this work flat outputs need to be measured.Faults affecting the actuators are considered rejected by the controller; by consequence reconfiguration is only carried out after a sensor fault occurs.Feasibility of the proposed approach is analyzed in two nonlinear plants, an unmanned quadrotor and a three tank system.

<p>Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models.</p><p>More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system.</p><p>In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented.</p><p>In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.</p><p>It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem.</p> / <p>Linjära tidsinvarianta approximationer av olinjära system har många användningsområden och kan tas fram på flera sätt. Om man har mätningar av in- och utsignalerna från ett olinjärt system kan man till exempel använda systemidentifiering och prediktionsfelsmetoden för att skatta en linjär modell utan att ta hänsyn till att systemet egentligen är olinjärt. Ett av huvudmålen med den här avhandlingen är att beskriva egenskaper för sådana approximativa modeller.</p><p>Framförallt studeras linjära tidsinvarianta modeller som är optimala approximationer i meningen att de minimerar ett kriterium baserat på medelkvadratfelet. Brusmodeller kan inkluderas i dessa modelltyper och både fallet med och utan brusmodell studeras här. Modeller som är optimala i medelkvadratfelsmening visar sig kunna uppvisa ett antal intressanta, men ibland oönskade, egenskaper. Bland annat visas det att en optimal linjär modell kan vara mycket känslig för små olinjäriteter. Denna känslighet är inte önskvärd i de flesta tillämpningar och innebär att en linjär approximation av ett nästan linjärt system kan vara oanvändbar för till exempel robust reglerdesign. Vidare visas det att en del valideringsmetoder som är framtagna för linjära system inte alltid kan användas för validering av linjära approximationer av olinjära system.</p><p>Man kan dock göra de optimala linjära modellerna mer användbara genom att välja lämpliga insignaler. Bland annat visas det att minfasfiltrerat vitt brus i många avseenden är ett bra val av insignal. Klassen av separabla signaler detaljstuderas också. Denna klass innehåller till exempel alla gaussiska signaler och just dessa signaler visar sig vara speciellt användbara för att ta fram approximationer av generaliserade wiener-hammerstein-system. Dessutom visas det att en viss typ av slumpmässiga multisinussignaler är separabel. Några teoretiska resultat om nästan linjära system presenteras också.</p><p>De flesta metoder för robust reglerdesign kan bara användas om storleken på modellfelet är känd för alla tänkbara insignaler. Detta är emellertid ofta inte realistiskt när ett olinjärt system approximeras med en linjär modell. I denna avhandling beskrivs därför ett alternativt sätt att göra en robust reglerdesign baserat på en tidsdiskret modell och en modellfelsmodell som bara är giltig för begränsade insignaler.</p><p>Ibland skulle det vara önskvärt om en linjär modell av ett system inte påverkades av förekomsten av små olinjäriteter i systemet. Denna oönskade påverkan kan i vissa fall reduceras om en liten olinjär term tas med i modellen. En identifieringsmetod för olinjära autoregressiva system med externa insignaler där denna möjlighet finns beskrivs här. Med hjälp av denna metod kan modeller som består av en parametrisk linjär del och en ickeparametrisk lipschitzkontinuerlig olinjär del skattas genom att man löser ett konvext optimeringsproblem.</p>

Nonlinear dynamical systems theory has inspired a new set of useful tools to be applied in climate studies. In this work we presented specific examples where information has been gained by the application of methods from nonlinear dynamical systems theory. The main goal is to understand the relative importance of stochastic forcing versus deterministic coupling within the context of Coupled General Circulation Models. This work address this important subject by approaching this goal through the development of a hierarchy of models with increasing complexity that we assert contain the essential dynamics of ENSO. We examined the effect of noise in a low order model and found that it is not restricted to blurring the attractor trajectories in phase space, but includes important changes in the dynamics of the system. The main results indicate that the presence of noise in a nonlinear system has two different effects. The presence of noise acts to increase the maximum Lyapunov exponent and can result in noise induced chaos if the system was originally stable. However, the same arguments are not valid if the original system is already in the chaotic regime, where the noise inclusion acts to decrease the maximum Lyapunov exponent, therefore increasing the system stability. The system of interest includes coupled ocean-atmosphere interactions and here we mimic this interaction by coupling two low order models with very different dominant time scales. These subsystems interact in a complex, nonlinear way and the behavior of the whole system cannot be explained by a linear summation of dynamics of the system parts. We used information theory concepts to detect the influence of the slow system dynamics in synchronizing the fast system in coupled models. We introduced a fast-slow coupled system, where both the slowness of the ocean model and the intensity of the boundary forcing anomalies contribute to the asymmetry and phase locking of both subsystems. The mechanisms controlling the fast modelspread were uncovered revealing uncertainty dynamics depending on the location of ensemble members in the model’s phase space. As an intermediate step between low order models and CGCMs we study the effect of noise on an intermediate complexity model. The addition of gaussian noise to the Zebiak-Cane model in order to understand the effects of noise on its attractor led to a way of estimating the noise level based on the effects of noise on the correlation dimension curves. We investigate the intrinsic predictability of the coupled models used here, and the different time scales associated with fast and slow modes were detected using the Finite Size Lyapunov Exponents. We found new estimates for the prediction horizon of ENSO for the Zebiak-Cane model as well as for the NCAR CCSM3 model and observations. The whole analysis of observations and CCSM3 was possible after applying noise reduction techniques. We also improved our understanding of three different noise reduction techniques by comparing the Local Projective Noise Reduction, the Interactive Ensemble strategy, and a Random Interactive Ensemble applied to CCSM3. The main difference between these two noise reduction techniques is when the process is applied. The Local Projective Noise Reduction can be applied to both model and observations, and it is done a posteriori in phase space, therefore the trajectories to be adjusted already posses the physical mechanisms embedded in them. The Interactive Ensemble approach can only be applied to model simulations and has shown to be a very useful technique for noise reduction since its done a priori while the system evolves instead of a posteriori, besides the fact that it allows to retrieve the spatial distribution of the noise level in physical space.

Nichtlineare multistabile Systeme unter dem Einfluss von Rauschen weisen vielschichtige dynamische Eigenschaften auf. <br /> Ein mittleres Rauschlevel zeitigt ein Springen zwischen den metastabilen Zustaenden. <br /> Dieser “attractor-hopping” Prozess ist gekennzeichnet durch laminare Bewegung in der Naehe von Attraktoren und erratische Bewegung, die sich auf chaotischen Satteln abspielt, welche in die fraktalen Einzugsgebietsgrenzen eingebettet sind. Er hat rauschinduziertes Chaos zur Folge. <br /> Bei der Untersuchung der dissipativen Standardabbildung wurde das Phaenomen der Praeferenz von Attraktoren durch die Wirkung des Rauschens gefunden. Dies bedeutet, dass einige Attraktoren eine groessere Wahrscheinlichkeit erhalten aufzutreten, als dies fuer das rauschfreie System der Fall waere. Bei einer bestimmten Rauschstaerke ist diese Bevorzugung maximal. <br /> Andere Attraktoren werden aufgrund des Rauschens weniger oft angelaufen. Bei einer entsprechend hohen Rauschstaerke werden sie komplett ausgeloescht. <br /> Die Komplexitaet des Sprungprozesses wird fuer das Modell zweier gekoppelter logistischer Abbildungen mit symbolischer Dynamik untersucht. <br /> Bei Variation eines Parameters steigt an einem bestimmten Wert des Parameters die topologische Entropie steil an, die neben der Shannon Entropie als Komplexitaetsmass verwendet wird. Dieser Anstieg wird auf eine neuartige Bifurkation von chaotischen Satteln zurueckgefuehrt, die in einem Verschmelzen zweier Sattel besteht und durch einen “Snap-back”-Repellor vermittelt wird. <br /> Skalierungsgesetze sowohl der Verweilzeit auf einem der zuvor getrennten Teile des Sattels als auch des Wachsens der fraktalen Dimension des entstandenen Sattels beschreiben diese neuartige Bifurkation genauer. <br /> Wenn ein chaotischer Sattel eingebettet in der offenen Umgebung eines Einzugsgebietes eines metastabilen Zustandes liegt, fuehrt das zu einer deutlichen Senkung der Schwelle des rauschinduzierten Tunnelns. <br /> Dies wird anhand der Ikeda-Abbildung, die ein Lasersystem mit einer zeitverzoegerden Interferenz beschreibt, demonstriert. Dieses Resultat wird unter Verwendung der Theorie der Quasipotentiale erzielt. <br /> Sowohl dieser Effekt, die Senkung der Schwelle für rauschinduziertes Tunneln aus einem metastabilen Zustand durch einen chaotischen Sattel, als auch die beiden Skalierungsgesteze sind von experimenteller Relevanz. / Nonlinear multistable systems under the influence of noise exhibit a plethora of interesting dynamical properties. A medium noise level causes hopping between the metastable states. This attractorhopping process is characterized through laminar motion in the vicinity of the attractors and erratic motion taking place on chaotic saddles, which are embedded in the fractal basin boundary. This leads to noise-induced chaos. The investigation of the dissipative standard map showed the phenomenon of preference of attractors through the noise. It means, that some attractors get a larger probability of occurrence than in the noisefree system. For a certain noise level this prefernce achieves a maximum. Other attractors are occur less often. For sufficiently high noise they are completely extinguished. The complexity of the hopping process is examined for a model of two coupled logistic maps employing symbolic dynamics. With the variation of a parameter the topological entropy, which is used together with the Shannon entropy as a measure of complexity, rises sharply at a certain value. This increase is explained by a novel saddle merging bifurcation, which is mediated by a snapback repellor. Scaling laws of the average time spend on one of the formerly disconnected parts and of the fractal dimension of the connected saddle describe this bifurcation in more detail. If a chaotic saddle is embedded in the open neighborhood of the basin of attraction of a metastable state, the required escape energy is lowered. This enhancement of noise-induced escape is demonstrated for the Ikeda map, which models a laser system with time-delayed feedback. The result is gained using the theory of quasipotentials. This effect, as well as the two scaling laws for the saddle merging bifurcation, are of experimental relevance.

No description available.

Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models. More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system. In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented. In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs. It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem. / Linjära tidsinvarianta approximationer av olinjära system har många användningsområden och kan tas fram på flera sätt. Om man har mätningar av in- och utsignalerna från ett olinjärt system kan man till exempel använda systemidentifiering och prediktionsfelsmetoden för att skatta en linjär modell utan att ta hänsyn till att systemet egentligen är olinjärt. Ett av huvudmålen med den här avhandlingen är att beskriva egenskaper för sådana approximativa modeller. Framförallt studeras linjära tidsinvarianta modeller som är optimala approximationer i meningen att de minimerar ett kriterium baserat på medelkvadratfelet. Brusmodeller kan inkluderas i dessa modelltyper och både fallet med och utan brusmodell studeras här. Modeller som är optimala i medelkvadratfelsmening visar sig kunna uppvisa ett antal intressanta, men ibland oönskade, egenskaper. Bland annat visas det att en optimal linjär modell kan vara mycket känslig för små olinjäriteter. Denna känslighet är inte önskvärd i de flesta tillämpningar och innebär att en linjär approximation av ett nästan linjärt system kan vara oanvändbar för till exempel robust reglerdesign. Vidare visas det att en del valideringsmetoder som är framtagna för linjära system inte alltid kan användas för validering av linjära approximationer av olinjära system. Man kan dock göra de optimala linjära modellerna mer användbara genom att välja lämpliga insignaler. Bland annat visas det att minfasfiltrerat vitt brus i många avseenden är ett bra val av insignal. Klassen av separabla signaler detaljstuderas också. Denna klass innehåller till exempel alla gaussiska signaler och just dessa signaler visar sig vara speciellt användbara för att ta fram approximationer av generaliserade wiener-hammerstein-system. Dessutom visas det att en viss typ av slumpmässiga multisinussignaler är separabel. Några teoretiska resultat om nästan linjära system presenteras också. De flesta metoder för robust reglerdesign kan bara användas om storleken på modellfelet är känd för alla tänkbara insignaler. Detta är emellertid ofta inte realistiskt när ett olinjärt system approximeras med en linjär modell. I denna avhandling beskrivs därför ett alternativt sätt att göra en robust reglerdesign baserat på en tidsdiskret modell och en modellfelsmodell som bara är giltig för begränsade insignaler. Ibland skulle det vara önskvärt om en linjär modell av ett system inte påverkades av förekomsten av små olinjäriteter i systemet. Denna oönskade påverkan kan i vissa fall reduceras om en liten olinjär term tas med i modellen. En identifieringsmetod för olinjära autoregressiva system med externa insignaler där denna möjlighet finns beskrivs här. Med hjälp av denna metod kan modeller som består av en parametrisk linjär del och en ickeparametrisk lipschitzkontinuerlig olinjär del skattas genom att man löser ett konvext optimeringsproblem.

Differential-algebraic equations (DAEs) form the natural way in which models of physical systems are delivered from an object-oriented modeling tool like Modelica. Differential-algebraic equations are also known as descriptor systems, singular systems, and implicit systems. If some constant parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. It may also be of interest to estimate the value of time-varying variables in the model. This is often referred to as state estimation. The objective of this work is to examine how gray box identification and estimation of time-varying variables can be performed for models described by differential-algebraic equations. If a model has external stimuli that are not measured or uncertain measurements, it is often appropriate to model this as stochastic processes. This is called noise modeling. Noise modeling is an important part of system identification and state estimation, so we examine how well-posedness of noise models for differential-algebraic equations can be characterized. For well-posed models, we then discuss how particle filters can be implemented for estimation of time-varying variables. We also discuss how constant parameters can be estimated. When estimating time-varying variables, it is of interest to examine if the problem is observable, that is, if it has a unique solution. The corresponding property when estimating constant parameters is identifiability. In this thesis, we discuss how observability and identifiability can be determined for DAEs. We propose three approaches, where one can be seen as an extension of standard methods for state-space systems based on rank tests. For linear DAEs, a more detailed analysis is performed. We use some well-known canonical forms to examine well-posedness of noise models and to implement estimation of time-varying variables and constant parameters. This includes formulation of Kalman filters for linear DAE models. To be able to implement the suggested methods, we show how the canonical forms can be computed using numerical software from the linear algebra package LAPACK.

Identification of nonlinear dynamical models of a black box nature involves both structure decisions (i.e., which regressors to use and the selection of a regressor function), and the estimation of the parameters involved. The typical approach in system identification is often a mix of all these steps, which for example means that the selection of regressors is based on the fits that is achieved for different choices. Alternatively one could then interpret the regressor selection as based on hypothesis tests (F-tests) at a certain confidence level that depends on the data. It would in many cases be desirable to decide which regressors to use, independently of the other steps. A survey of regressor selection methods used for linear regression and nonlinear identification problems is given. In this thesis we investigate what the well known method of analysis of variance (ANOVA) can offer for this problem. System identification applications violate many of the ideal conditions for which ANOVA was designed and we study how the method performs under such non-ideal conditions. It turns out that ANOVA gives better and more homogeneous results compared to several other regressor selection methods. Some practical aspects are discussed, especially how to categorise the data set for the use of ANOVA, and whether to balance the data set used for structure identification or not. An ANOVA-based method, Test of Interactions using Layout for Intermixed ANOVA (TILIA), for regressor selection in typical system identification problems with many candidate regressors is developed and tested with good performance on a variety of simulated and measured data sets. Typical system identification applications of ANOVA, such as guiding the choice of linear terms in the regression vector and the choice of regime variables in local linear models, are investigated. It is also shown that the ANOVA problem can be recast as an optimisation problem. Two modified, convex versions of the ANOVA optimisation problem are then proposed, and it turns out that they are closely related to the nn-garrote and wavelet shrinkage methods, respectively. In the case of balanced data, it is also shown that the methods have a nice orthogonality property in the sense that different groups of parameters can be computed independently.

Noise contribution in nonlinear systems is very different from that in linear systems. The noise effects in nonlinear systems can be complicated and not obvious to predict. In this thesis, the focus was on the noise contribution in nonlinear systems when measuring with the nonlinear vector network analyzer (NVNA). An additional noise source together with a single sinewave signal was fed into the input of the amplifier and the performance was studied. The input power of the amplifier is considered to be the sum of the noise power and the signal power. The variation of the 1 dB compression point and the third order interception point as functions of the added noise power were studied. From the measured results in this thesis, the 1 dB compression point referred to the output power will decrease when increasing the added noise power at the input of the amplifier. The contribution of the added noise to the 1 dB compression point of an amplifier is considered dual: with the added noise the linear regression lines of the AM/AM curves are changed, and due to hard clipping the useful output power is reduced. As a result of those two effects, the added noise made the compression start at a lower power level. When the added noise reaches a certain level, the 1 dB compression point is hard to measure. Thus when performing nonlinear measurements, the noise effects should be taken into considerations and further studies are required to get better understanding of the system’s behavior in noisy environment.

Recent advances in sensor and microcomputer technology and in control and aeroydynamics theories has made small unmanned aerial vehicles a reality. The small size, low cost and manoueverbility of these systems has positioned them to be potential solutions in a large class of applications. However, the small size of these vehicles pose significant challenges. The small sensors used on these systems are much noisier than their larger counterparts.The compact structure of these vehicles also makes them more vulnerable to environmental effects. This work develops several different control strategies for two sUAV platforms and provides the rationale for judging each of the controllers based on a derivation of the dynamics, simulation studies and experimental results where possible. First, the coaxial helicopter platform is considered. This sUAV’s dual rotor system (along with its stabilizer bar technology) provides the ideal platform for safe, stable flight in a compact form factor. However, the inherent stability of the vehicle is achieved at the cost of weaker control authority and therefore an inability to achieve aggressive trajectories especially when faced with heavy wind disturbances. Three different linear control strategies are derived for this platform. PID, LQR and H∞ methods are tested in simulation studies. While the PID method is simple and intuitive, the LQR method is better at handling the decoupling required in the system. However the frequency domain design of the H∞ control method is better at suppressing disturbances and tracking more aggressive trajectories. The dynamics of the quadrotor are much faster than those of the coaxial helicopter. In the quadrotor, four independent fixed pitch rotors provide the required thrust. Differences between each of the rotors creates moments in the roll, pitch and yaw directions. This system greatly simplifies the mechanical complexity of the UAV, making quadrotors cheaper to maintain and more accessible. The quadrotor dynamics are derived in this work. Due to the lack of any mechanical stabilization system, these quadrotor dynamics are not inherently damped around hover. As such, the focus of the controller development is on using nonlinear techniques. Linear quadratic regulation methods are derived and shown to be inadequate when used in zones moderately outside hover. Within nonlinear methods, feedback linearization techniques are developed for the quadrotor using an inner/outer loop decoupling structure that avoids more complex variants of the feedback linearization methodology. Most nonlinear control methods (including feedback linearization) assume perfect knowledge of vehicle parameters. In this regard, simulation studies show that when this assumption is violated the results of the flight significantly deteriorate for quadrotors flying using the feedback linearization method. With this in mind, an adaptation law is devised around the nonlinear control method that actively modifies the plant parameters in an effort to drive tracking errors to zero. In simple cases with sufficiently rich trajectory requirements the parameters are able to adapt to the correct values (as verified by simulation studies). It can also adapt to changing parameters in flight to ensure that vehicle stability and controller performance is not compromised. However, the direct adaptive control method devised in this work has the added benefit of being able to modify plant parameters to suppress the effects of external disturbances as well. This is clearly shown when wind disturbances are applied to the quadrotor simulations. Finally, the nonlinear quadrotor controllers devised above are tested on a custom built quadrotor and autopilot platform. While the custom quadrotor is able to fly using the standard control methods, the specific controllers devised here are tested on a test bench that constrains the movement of the vehicle. The results of the tests show that the controller is able to sufficiently change the necessary parameter to ensure effective tracking in the presence of unmodelled disturbances and measurement error.