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This thesis presents the integration of reproducing kernel Hilbert spaces (RKHSs) into the model reference adaptive control (MRAC) framework to enhance the control systems of quadcopters. Traditional MRAC systems, while robust under predictable conditions, can struggle with the dynamic uncertainties typical in unmanned aerial vehicle (UAV) operations such as wind gusts and payload variations. By incorporating RKHS, we introduce a non-parametric, data-driven approach that significantly enhances system adaptability to in-flight dynamics changes. The research focuses on the design, simulation, and analysis of an RKHS-enhanced MRAC system applied to quadcopters. Through theoretical developments and simulation results, the thesis demonstrates how RKHS can be used to improve the precision, adaptability, and error handling of MRAC systems, especially in managing the complexities of UAV flight dynamics under various disturbances. The simulations validate the improved performance of the RKHS-MRAC system compared to traditional MRAC, showing finer control over trajectory tracking and adaptive gains. Further contributions of this work include the exploration of the computational impact and the relationship between the configuration of basis centers and system performance. Detailed analysis reveals that the number and distribution of basis centers critically influence the system's computational efficiency and adaptive capability, demonstrating a significant trade-off between efficiency and performance. The thesis concludes with potential future research directions, emphasizing the need for further tests and implementations in real-world scenarios to explore the full potential of RKHS in adaptive UAV control, especially in critical applications requiring high precision and reliability. This work lays the groundwork for future explorations into scalable RKHS applications in MRAC systems, aiming to optimize computational resources while maximizing control system performance. / Master of Science / This thesis develops and tests an advanced flight control system for quadcopters, using a technique referred to as reproducing kernel Hilbert space (RKHS) embedded model reference adaptive control (MRAC). Traditional control systems perform well in stable conditions but often falter with environmental challenges such as wind gusts or changes in weight. By integrating RKHS into MRAC, this new controller adapts in real-time, instantly adjusting the drone's operations based on its performance and environmental interactions. The focus of this research is on the creation, testing, and analysis of this enhanced control system. Results from simulations show that incorporating RKHS into standard MRAC significantly boosts precision, adaptability, and error management, particularly under the complex flight dynamics faced by unmanned aerial vehicles (UAVs) in varied environments. These tests confirm that the RKHS-MRAC system performs better than traditional approaches, especially in maintaining accurate flight paths. Additionally, this work examines the computational costs and the impact of various RKHS configurations on system performance. The thesis concludes by outlining future research opportunities, stressing the importance of real-world tests to verify the ability of RKHS-embedded MRAC in critical real-world applications where high precision and reliability are essential.

In this dissertation, two main topics are explored, the vehicle routing problem (VRP) and model reference adaptive control (MRAC) for unknown nonlinear systems. The VRP and its extension, the split delivery VRP (SVRP), are analyzed to determine the effects of using two different objective functions, the total cost objective, and the last delivery objective. A worst-case analysis suggests that using the SVRP can improve total costs by as much as a factor of 2 and the last delivery by a factor that scales with the number of vehicles over the classical VRP. To test the theoretical worst-cases against the solutions of benchmark datasets, a heuristic is developed based on embedding a random variable neighborhood search within an iterative local search heuristic. Results suggest that the split deliveries do in fact improve total cost and last delivery times over the classical formulation. The SVRP has been developed classically for use with vehicles such as trucks which have large payload capacities and typically long ranges for deliveries, but are limited to traversing on roads. Unmanned aerial vehicles (UAVs) are useful for their high maneuverability, but suffer from limited capacity for payloads and short ranges. The classical SVRP formulation is extended to one more suitable for UAVs by accounting for limited range, limited payloads, and the ability to swap batteries at known locations. Instead of Euclidean distances, path plans which are adjusted for a known, constant wind underlie the cost matrix of the optimization problem. The effects of payload on the vehicle's range are developed using propeller momentum theory, and simulations verify that the proposed approach could be used in a realistic scenario. Two novel MRAC laws are then developed. The first, MRAC laws for prescribed performance, exploits barrier Lyapunov functions and a 2-Layer approach to guarantee user-defined performance. This control law allows unknown nonlinear systems to verify a user-defined rate of convergence of the tracking error while verifying apriori control and tracking error constraints. Numerical simulations are performed on the roll dynamics of a delta-wing aircraft. The second novel MRAC law is MRAC for switched dynamical systems which is proven in two different mathematical frameworks. Applying the Caratheodory framework, it is proven that if the switching signal has an arbitrarily small, but non-zero, dwell-time, then solutions of both the trajectory tracking error's and the adaptive gains' dynamics exist, are unique, and are defined almost everywhere, and the trajectory tracking error converges asymptotically to zero. Employing the Filippov framework, it is proven that if the switching signal is Lebesgue integrable and has countably many points of discontinuity, then maximal solutions of both the trajectory tracking error and the adaptive gains dynamics exist and are defined almost everywhere, and the trajectory tracking error converges to zero asymptotically. The proposed MRAC law is experimentally verified in the case where a UAV with tilting propellers is tasked with mounting an unknown camera onto a wall. The previous results are then combined into a novel application in construction. A method for using a UAV to measure autonomously the moisture of an exterior precast concrete envelope is developed which can provide data feedback through contact-based measurements to improve safety and real-time data acquisition through the integration with the Building Information Model (BIM). To plan the path of the vehicle, the path planning and SVRP for UAV approaches developed in previous chapters are utilized. To enable the UAS to contact surfaces, a switched MRAC law is employed to control the vehicle throughout and guarantee successful measurements. A full physics-based simulation environment is developed, and the proposed framework is used to simulate taking multiple measurements. / Doctor of Philosophy / The main goal of this dissertation is to provide an implementable approach to the routing and control problem for unmanned aerial vehicles (UAVs) tasked with delivering payloads or taking images or videos of known locations. To plan routes for the fleet of vehicles, a split vehicle routing (SVRP) approach is utilized. UAVs are useful for their high maneuverability, but suffer from limited capacity for payloads and short ranges. Before extending the SVRP to a formulation more suitable for UAVs, we study the effects of using two different objective functions on the solutions to the optimization problem through a worst-case analysis. Namely, we study the minimum total cost function and the minimum last delivery function and their effects on both the classical vehicle routing problem (VRP), where only one vehicle can visit each customer, and the SVRP, where multiple vehicles can visit each customer. A custom heuristic is developed to solve several benchmark instances, and the results suggest that using the SVRP can save in total cost and last delivery over the VRP when using the same objective functions. The classical SVRP formulation is then extended to one more suitable for UAVs by accounting for limited range, limited payloads, and the ability to swap batteries at known locations. Instead of using straight line approaches to traversing between locations, a path planning approach is utilized and wind is accounted for. The effects of payload on the vehicle's range are also considered, and simulations verify that the proposed approach could be used in a realistic scenario. After developing a routing approach for UAVs, the control problem is considered. The first control approach developed is for unknown nonlinear systems which necessitate control and tracking error constraints that can be set before the start of the mission. This result is achieved using a novel model reference adaptive control (MRAC) approach. In addition to verifying the constraints, a drawback of classical MRAC approaches, the poor performance in the transient stages, is addressed by providing the ability to guarantee a user-defined rate of convergence of the system. Numerical simulations are performed on the roll dynamics of a delta-wing aircraft. A second MRAC approach is then developed for the cases in which the UAVs may be tasked with installing a payload at the customer location. An approach is used where the vehicles are considered to have different flight states, one where the vehicle is in free flight, and one where the vehicle contacts the wall. These types of systems are denoted as switched dynamical systems, and an adaptive control law is developed for unknown nonlinear switched plants that must follow the trajectory of user-defined linear switched reference models. The proposed MRAC law is experimentally verified in the case where a UAV with tilting propellers is tasked with mounting an unknown camera onto a wall. Finally, we seek to combine the new routing and control approach into an application to improve safety within a construction site. A method for using a UAV to measure autonomously the moisture of an exterior precast concrete envelope is developed which can provide data feedback through contact-based measurements to improve safety and real-time data acquisition through the integration with the Building Information Model (BIM). To plan the path of the vehicle, the path planning and SVRP for UAV approaches developed in previous chapters are utilized. To enable the UAS to contact surfaces, a switched MRAC law is employed to control the vehicle throughout and guarantee successful measurements. A full physics-based simulation environment is developed, and the proposed framework is used to simulate taking multiple measurements.

Control systems for robotic manipulators have been investigated for several years. The difficulty in designing a controller for a robotic manipulator is due to the highly nonlinear, time-varying dynamics. Closed-loop constant gain controllers are effective when the robot is expected to perform a limited range of operations. In the case of a mobile robot, the commanded tasks are not likely to be repetitive. Thus, another method of control is desired to overcome the effects of the nonlinear time-varying dynamics. Several adaptive control methods have been applied to robotic manipulators. The adaptive controllers are successful at trajectory tracking in the presence of the nonlinear time-varying dynamics. Some of these methods are computationally demanding, therefore, most of the current research focuses on efficient adaptive control methods. In particular, the area of decentralized adaptive control is gaining popularity. This method involves reducing a dynamic system into subsystems, each with an individual controller. This method is more efficient since the controllers can operate simultaneously. In this study, a decentralized model reference adaptive controller (MRAC) was designed for a four-degree-of-freedom mobile robot. The performance of the decentralized MRAC controller was compared to that of a constant gain state feedback controller. The decentralized MRAC control strategy proved to be an efficient method of control for a mobile robot that is superior to state feedback control when the robot is performing highly nonlinear time-varying tasks. Also, the computational load for each subsystem of the decentralized controller was less than the computational load of the state feedback controller. / Master of Science

Adaptive controllers allow robots to perform a wide variety of tasks, but the extensive computations required have generated an interest in developing decentralized adaptive controllers. Horner has designed an adaptive controller for a four-degree-of-freedom mobile robot and tested it through simulations. The study described in this thesis uses the techniques described by Horner to design and test a decentralized model reference adaptive controller (DMRAC) for a physical four-degree-of-freedom mobile robot. The study revealed several difficulties in implementing this design. Most notably, the robot available for the research did not allow for the measurement of joint velocity, so it was necessary to estimate the velocity as the derivative of the position measurement. The noise created by this estimation made completion of testing impossible. Future research should be performed on a robot that provides joint velocity measurement. Alternatively, a study could include state estimation as part of the controller, thus reducing and possibly eliminating the need for velocity measurement. / Master of Science

A presente tese tem por propósito contribuir para uma política de planejamento no campo da educação a distância (EAD). Para isto concebe uma proposta multi-modelo de referência lastreada na definição de estratégias em espectro de alta complexidade, que considera uma seqüência de procedimentos sistematizados nas seguintes fases: (i) Determinação das necessidades de informação, em duas etapas: (a) identificação dos fatores críticos de sucesso (FCS) e (b) identificação das áreas de informação; (ii) Determinação das competências, em três etapas: (a) determinação dos conhecimentos, (b) determinação das habilidades, e (c) determinação das atitudes; (iii) Determinação dos graus de avaliação de competências; (iv) Determinação das estratégias em redes de conhecimentos. Evidencia-se a aplicação a um estudo de caso nas concessões rodoviárias no Brasil, na perspectiva das parcerias público-privadas (PPPs). A consecução da pesquisa foi por meio da intervenção de especialistas e um grupo pequeno de estudantes de um programa de EAD (MBA) aplicado às PPPs. A coleta de dados foi por meio de um formulário semi-estruturado, do tipo escalar, em uma matriz de julgamento, com a intervenção de especialistas. Vários instrumentos de apoio foram utilizados na elaboração da modelagem, com vistas a reduzir a subjetividade dos resultados alcançados: escalagem psicométrica - Lei dos Julgamentos Categóricos de Thurstone (LJC), Multicriteriais-Compromise Programinng, Electre III, e Promethee II; Análise Multivariada; Krigagem, Redes Neurais Artificiais (RNA); Redes Neurofuzzy. Os resultados produzidos mostraram-se satisfatórios, validando o procedimento proposto para EAD. Procedimento este, fundamental na definição de programas destinados para planejar a capacitação de recursos humanos a distância, bem como para a constituição de outros elementos do capital intelectual em políticas de EAD. / This thesis intends to contribute to the planning guidelines in the field of distance education (DE). Thus, it develops a multi-model reference proposal supported by the definition of a highly complex spectrum of strategies that considers a sequence of systematic procedures in the following phases: (i) Determining the information needs in two stages: (a) identification of the critical success factors (CSF), and (b) identification of the information areas; (ii) Determination of competences in three stages, determining: (a) knowledge, (b) skills, and (c) attitudes; (iii) Determination of the degree of competence evaluation; and (iv) Determination of strategies in knowledge networks. There is the application to a case study of the road concessions in Brazil, within the perspective of public-private partnerships (PPPs). The research was achieved through the intervention of specialists and a small group of students from a DE program (MBA) applied to the PPPs. The data collection was conducted by means of a semi-structured form, the scalar type in a trial matrix, to which experts ascribed their assessments. Several support instruments were used in the modeling elaboration in order to reduce subjectivity in the results: psychometric scales - Thurstones Law of Comparative Judgment (LCJ), Multi-criteria Compromise Programming, Electre III, and Promethee II; Multivariate Analysis; Krigage, Artificial Neural Networking (ANN); Neuro-fuzzy networks. The results produced are satisfactory, validating the proposed procedure for DE. This is an essential procedure for the definition of programs designed to plan the training of human resources at a distance, as well as to establish other elements of intellectual capital for DE guidelines.

Métodos de controle por modelo de referência, usualmente encontrados na literatura de controle baseado em dados, têm como principal característica a especificação do desempenho desejado em malha fechada através de um modelo de referência. Estes métodos são, no entanto, comumente desenvolvidos para tratar o problema de seguimento de referência, em detrimento do comportamento relativo à perturbação de carga. Nesse sentido, recentemente foi desenvolvido o método de controle baseado em dados Virtual Disturbance Feedback Tuning – VDFT, que pode ser interpretado como um método de controle por modelo de referência para perturbação, em que o controlador é sintonizado para alcançar em malha fechada o comportamento regulatório especificado. A escolha no entanto do modelo de referência para perturbação mostra-se desafiadora, especialmente considerando o cenário em que pouca ou nenhuma informação sobre o modelo paramétrico do sistema está disponível. Dessa forma, este trabalho tem como objetivo estudar o impacto da escolha deste modelo sobre a sintonia do controlador utilizando o método VDFT e propor uma abordagem sistemática para lidar com essa variável de projeto. A solução aqui concebida é a de flexibilizar o modelo de referência para perturbação e identificar parte do seu numerador juntamente aos parâmetros do controlador que, associada a um conjunto de diretivas de projeto, permitem aproximar o comportamento em malha fechada do inicialmente especificado. Esse resultado viabiliza a utilização do método VDFT com critério flexível no contexto de uma estrutura hierárquica de controle, em que uma malha externa de controle preditivo é associada à malha de controle por VDFT, evitando a etapa de identificação de um modelo para o processo. Por fim, a formulação do método VDFT, assim como sua adaptação flexível, é estendida a fim de levar em conta processos multivariáveis. Experimentos e resultados em simulação ilustram as contribuições deste trabalho. / Model reference control methods, usually found within data-based control literature, have as main feature the specification of the desired closed-loop performance through a reference model. These methods are however commonly developed to address the set point tracking problem, to the disadvantage of load disturbance rejection. In this sense, the data-based control method Virtual Disturbance Feedback Tuning – VDFT was recently developed, which could be interpreted as a model reference control method for disturbance, in which the controller is tuned in order to reach in closed-loop the specified regulatory behavior. Nonetheless, the choice of the disturbance reference model is challenging, especially considering the scenario where little or no information on the process’ parametric model is available. This work aims therefore to study the impact of the disturbance reference model choice on the controller tuning using the VDFT method and to propose a systematic approach to deal with this design variable. The solution here conceived is to loosen the disturbance reference model and identify part of its numerator along with the controller parameters, which, associated with a set of design directions, allow the closed-loop behavior to be drawn closer to the one initially specified. This result enables the use of the VDFT method with flexible criterion in the context of a hierarchical control structure, in which an external predictive control loop is associated to the VDFT control loop, avoiding thus the identification of a process model. Finally, VDFT method’s formulation, as well as its flexible adaptation, is extended in order to take into account multivariable processes. Experiments and simulation results illustrate the contributions of this work.

A crescente complexidade do controle dos processos industriais vem exigindo sistemas de controle cada vez mais precisos, confiáveis e versáteis. No sentido de atender a estas exigências, algoritmos diversos de controle e estimação, tais como: técnicas de controle adaptativas, preditivas, estimação paramétrica, filtros de Kalman, observação de estados, etc. têm sido desenvolvidas, simuladas e implementadas com relativa facilidade nos modernos sistemas digitais. Este trabalho propõe uma estratégia de controle em redes Fieldbus usando controle adaptativo por modelo de referência através de variáveis de estado, para resolver sistemas complexos. O algoritmo de controle proposto é composto por um observador de estados trabalhando em conjunto com um esquema de controle adaptativo por modelo de referência. As malhas de controle no Fieldbus consistem em um conjunto de blocos funcionais padrões existentes, conectados aos novos blocos funcionais propostos e desenvolvidos de acordo com as especificações da norma Fieldbus Foundation. Este algoritmo de controle realiza os cálculos de maneira distribuída entre os dispositivos da rede Fieldbus, implicando em várias vantagens, tais como: a) perda do supervisório não implica na perda do algoritmo de controle, b) menor tráfego de dados na rede, c) algoritmo de controle que não depende do tempo de processamento do computador. Os resultados dos testes obtidos são apresentados e demonstraram um alto grau de precisão, destacando-se a estabilidade e aplicabilidade do algoritmo proposto. / The rising complexity of the industrial control processes has been claiming more and more accurate, reliable and versatile control systems. Attempting to satisfy this demand, several control and estimation systems algorithms, such as adaptive and predictive techniques, parametric estimation, Kalman filtering, state observation, have been designed, simulated and implemented with relative easiness in the modern digital systems. This work proposes a new control strategy in Fieldbus networks, using adaptive control techniques through state variables, to solve complex systems. The proposed control algorithm is based on an states observer concurrently working with a reference model adaptive control scheme. The modified Fieldbus network consists of a set of standard function blocks, connected to the proposed new function blocks. These new function blocks comply with the specifications of the Fieldbus Foundation norm. This control algorithm accomplishes its calculation in a distributed way among the fieldbus devices. This operating feature results in some advantages, such as: any failure in the supervisory system does not imply in the loss of the control algorithm, b) a lower data transmission in the network, c) control algorithm that does not depend on the processing time of the computer. The obtained results corroborate with the expected advantages of the proposed algorithm, in terms of high degree of accuracy, stability and applicability.

Prohibitive cost and large size of conventional angular rate sensors have limited their use to large scale aeronautical applications. However, the emergence of MEMS technology in the last two decades has enabled angular rate sensors to be fabricated that are orders of magnitude smaller in size and in cost. The reduction in size and cost has subsequently encouraged new applications to emerge, but the accuracy and resolution of MEMS angular rate sensors will have to be greatly improved before they can be successfully utilised for such high end applications as inertial navigation. MEMS angular rate sensors consist of a vibratory structure with two main resonant modes and high Q factors. By means of an external excitation, the device is driven into a constant amplitude sinusoidal vibration in the first mode, normally at resonance. When the device is subject to an angular rate input, Coriolis acceleration causes a transfer of energy between the two modes and results in a sinusoidal motion in the second mode, whose amplitude is a measure of the input angular rate. Ideally the only coupling between the two modes is the Coriolis acceleration, however fabrication imperfections always result in some cross stiffness and cross damping effects between the two modes. Much of the previous research work has focussed on improving the physical structure through advanced fabrication techniques and structural design; however attention has been directed in recent years to the use of control strategies to compensate for these structural imperfections. The performance of the MEMS angular rate sensors is also hindered by the effects of time varying parameter values as well as noise sources such as thermal-mechanical noise and sensing circuitry noise. In this thesis, MEMS angular rate sensing literature is first reviewed to show the evolu- tion of MEMS angular rate sensing from the basic principles of open-loop operation to the use of complex control strategies designed to compensate for any fabrication imperfections and time-varying effects. Building on existing knowledge, a novel adaptively controlled MEMS triaxial angular rate sensor that uses a single vibrating mass is then presented. Ability to sense all three components of the angular rate vector with a single vibrating mass has advantages such as less energy usage, smaller wafer footprint, avoidance of any mechanical interference between multiple resonating masses and removal of the need for precise alignment of three separate devices. The adaptive controller makes real-time estimates of the triaxial angular rates as well as the device cross stiffness and cross damping terms. These estimates are then used to com- pensate for their effects on the vibrating mass, resulting in the mass being controlled to follow a predefined reference model trajectory. The estimates are updated using the error between the reference model trajectory and the mass's real trajectory. The reference model trajectory is designed to provide excitation to the system that is sufficiently rich to enable all parameter estimates to converge to their true values. Avenues for controller simplification and optimisation are investigated through system simulations. The triaxial controller is analysed for stability, averaged convergence rate and resolution. The convergence rate analysis is further utilised to determine the ideal adaptation gains for the system that minimises the unwanted oscillatory behaviour of the parameter estimates. A physical structure for the triaxial device along with the sensing and actuation means is synthesised. The device is realisable using MEMS fabrication techniques due to its planar nature and the use of conventional MEMS sensing and actuation elements. Independent actuation and sensing is achieved using a novel checkerboard electrode arrangement. The physical structure is refined using a design automation process which utilises finite element analysis (FEA) and design optimisation tools that adjust the design variables until suitable design requirements are met. Finally, processing steps are outlined for the fabrication of the device using a modified, commercially available polysilicon MEMS process.

This dissertation is an initial study of how modern engineering control may be applied to reverse engineer homeostasis in metabolic pathways using high-throughput biological data. This attempt to reconcile differences between engineering control and biological homeostasis from an interdisciplinary perspective is motivated not only by the observation that robust behavior in metabolic pathways resembles stabilized dynamics in controlled systems, but also by the challenges forewarned in achieving a true meeting of minds between engineers and biologists. To do this, a comparator model is developed and applied to model the effect of single-gene (SPT) overexpression on C16:0 sphingolipid de novo biosynthesis in vitro, specifically to simulate and predict potential homeostatic pathway interactions between the sphingolipid metabolites. Sphingolipid de novo biosynthesis is highly regulated because its pathway intermediates are highly bioactive. Alterations in sphingolipid synthesis, storage, and metabolism are implicated in human diseases. In addition, when variation in structure is considered, sphingolipids are one of the most diverse and complex families of biomolecules. To complete the modeling paradigm, wild type cells are defi ned as the reference that exhibits the "desired" pathway dynamics that the treated cells approach. Key model results show that the proposed modern engineering control approach using a comparator to reverse engineer homeostasis in metabolic systems is: (a) eff ective in capturing observed pathway dynamics from experimental data, with no signifi cant di fference in precision from existing models, (b) robust to potential errors in estimating state-space parameters as a result of sparse data, (c) generalizable to model other metabolic systems, as demonstrated by testing on a separate independent dataset, and (d) biologically relevant in terms of predicting steady-state feedback as a result of homeostasis that is verifi ed in literature and with additional independent data from drug dosage experiments.