CAPES / O objetivo desta dissertação é propor uma técnica para a síntese via realimentação de estados para sistemas lineares e invariantes no tempo, considerando que os estados realimentados são previamente quantizados. Para tanto, o erro de quantização é inicialmente modelado como um ruído externo. Assim, o problema de obter os ganhos de realimentação de estados, se torna um problema de projetar os ganhos que minimizem a norma H¥ do sistema controlado. Os ganhos de realimentação são calculados pela solução de um conjunto de condições descritas na forma de desigualdades matriciais lineares. A técnica é ilustrada pela aplicação da realimentação de estados quantizada em um servomecanismo. / The main objective of this dissertation is to propose a technique for synthesis by statefeedback for linear time-invariant systems, considering that the states are quantized before the feedback. To tackle such problem, the quantization error is initially modeled as an external noise. Therefore, the problem of getting the state-feedback gains, becomes a problem of designing the gains that minimize the H¥ norm of the system. The state-feedback gains are calculated by solving a set of conditions described in the form of linear matrix inequalities. The technique is illustrated by applying the of feedback of quantized states to a servo-mechanism.

Error-corecting codes are used during most of data transmissions these days. To save space, we would like to use codes which are able to correct enough errors without extending the message too much. The expander codes look promising - they are asymptotically optimal, however, in practice they are just too long. Better expander constructions could be achieved via randomness con- ductors. In this thesis, we explain what conductors are and which constructions are possible for them. In the end we will convert them to expanders and almost get expander codes which are short enough for practical use but nevertheless good. 1

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In this essay I use Mikhail Bakhtins theory of the chronotope to come to a deeper understanding of the spatio-temporal relationships in Momo and the Time Thieves. I use it to investigate the chronotopic structure of childhood, how it relates to the idea of the idyll, threshold experiences and heterotopic and liminal chronotopes. There is also a discussion on the function of mythic and linear time in building the narrative, and how Ende reverses and subverts some of the given patterns of myth, folklore and fantasy to create a dialogue between chronotopes and genres. / <p>Slutgiltigt godkännandedatum: 2023-05-31</p>

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Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed. / Ph. D.

This dissertation describes the development and modeling of a low-cost, open source, and reliable small fixed-wing unmanned aerial vehicle (UAV) for advanced control implementation. The platform is mostly constructed of low-cost commercial off-the-shelf (COTS) components. The only non-COTS components are the airdata probes which are manufactured and calibrated in-house, following a procedure provided herein. The airframe used is the commercially available radio-controlled 6-foot Telemaster airplane from Hobby Express. The airplane is chosen mainly for its adequately spacious fuselage and for being reasonably stable and sufficiently agile. One noteworthy feature of this platform is the use of two separate low-cost open source onboard computers for handling the data management/hardware interfacing and control computation. Specifically, the single board computer, Gumstix Overo Fire, is used to execute the control algorithms, whereas the autopilot, Ardupilot Mega, is mostly used to interface the Overo computer with the sensors and actuators. The platform supports multi-vehicle operations through the use of a radio modem that enables multi-point communications. As the goal of the development of this platform is to implement rigorous control algorithms for real-time trajectory tracking and distributed control, it is important to derive an appropriate flight dynamic model of the platform, based on which the controllers will be synthesized. For that matter, reasonably accurate models of the vehicle, servo motors and propulsion system are developed. Namely, the output error method is used to estimate the longitudinal and lateral-directional aerodynamic parameters from flight test data. The moments of inertia of the platform are determined using the simple pendulum test method, and the frequency response of each servomotor is also obtained experimentally. The Javaprop applet is used to obtain lookup tables relating airspeed to propeller thrust at constant throttle settings. Control systems are also designed for the regulation of this UAV along real-time trajectories. The reference trajectories are generated in real-time from a library of pre-specified motion primitives and hence are not known a priori. Two concatenated primitive trajectories are considered: one formed from seven primitives exhibiting a figure-8 geometric path and another composed of a Split-S maneuver that settles into a level-turn trim trajectory. Switched control systems stemming from l2-induced norm synthesis approaches are designed for discrete-time linearized models of the nonlinear UAV system. These controllers are analyzed based on simulations in a realistic operational environment and are further implemented on the physical UAV. The simulations and flight tests demonstrate that switched controllers, which take into account the effects of switching between constituent sub-controllers, manage to closely track the considered trajectories despite the various modeling uncertainties, exogenous disturbances and measurement noise. These switched controllers are composed of discrete-time linear sub-controllers designed separately for a subset of the pre-specified primitives, with the uncertain initial conditions, that arise when switching between primitives, incorporated into the control design. / Ph. D.

This dissertation studies the model reduction and distributed control problems for interconnected systems, i.e., systems that consist of multiple interacting agents/subsystems. The study of the analysis and synthesis problems for interconnected systems is motivated by the multiple applications that can benefit from the design and implementation of distributed controllers. These applications include automated highway systems and formation flight of unmanned aircraft systems. The systems of interest are modeled using arbitrary directed graphs, where the subsystems correspond to the nodes, and the interconnections between the subsystems are described using the directed edges. In addition to the states of the subsystems, the adopted frameworks also model the interconnections between the subsystems as spatial states. Each agent/subsystem is assumed to have its own actuating and sensing capabilities. These capabilities are leveraged in order to design a controller subsystem for each plant subsystem. In the distributed control paradigm, the controller subsystems interact over the same interconnection structure as the plant subsystems. The models assumed for the subsystems are linear time-varying or linear parameter-varying. Linear time-varying models are useful for describing nonlinear equations that are linearized about prespecified trajectories, and linear parameter-varying models allow for capturing the nonlinearities of the agents, while still being amenable to control using linear techniques. It is clear from the above description that the size of the model for an interconnected system increases with the number of subsystems and the complexity of the interconnection structure. This motivates the development of model reduction techniques to rigorously reduce the size of the given model. In particular, this dissertation presents structure-preserving techniques for model reduction, i.e., techniques that guarantee that the interpretation of each state is retained in the reduced order system. Namely, the sought reduced order system is an interconnected system formed by reduced order subsystems that are interconnected over the same interconnection structure as that of the full order system. Model reduction is important for reducing the computational complexity of the system analysis and control synthesis problems. In this dissertation, interior point methods are extensively used for solving the semidefinite programming problems that arise in analysis and synthesis. / Ph. D. / The work in this dissertation is motivated by the numerous applications in which multiple agents interact and cooperate to perform a coordinated task. Examples of such applications include automated highway systems and formation flight of unmanned aircraft systems. For instance, one can think of the hazardous conditions created by a fire in a building and the benefits of using multiple interacting multirotors to deal with this emergency situation and reduce the risks on humans. This dissertation develops mathematical tools for studying and dealing with these complex systems. Namely, it is shown how controllers can be designed to ensure that such systems perform in the desired way, and how the models that describe the systems of interest can be systematically simplified to facilitate performing the tasks of mathematical analysis and control design.

The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones. This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity. In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order can be reduced even further. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems. The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results. In the last part of the thesis, topics for future investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.