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Tailsitter UAVs (Unmanned Aerial Vehicles) are a type of VTOL (Vertical Take off and Landing) aircraft that combines the agility of a quadrotor drone with the endurance and speed of a fixed-wing aircraft. For this reason, they have become popular in a wide range of applications from tactical surveillance to parcel delivery. This thesis details a clean sheet design process for a tailsitter UAV that includes the dynamic modeling, control design, simulation, vehicle design, vehicle prototype fabrication, and testing of a tailsitter UAV. The goal of this process was to design a robust controller that is able to handle uncertainties in the system's parameters and external disturbances and subsequently can control the vehicle through the transition between vertical and horizontal flight regimes. It is evident in the literature that most researchers choose to model and control tailsitter UAVs using separate methods for the vertical and horizontal flight regimes and combine them into one control architecture. The novelty of this thesis is the use of a single dynamical model for all flight regimes and the robust control technique used. The control algorithm used for this vehicle is a MRAC (Model Reference Adaptive Control) law, which relies on reference models and gains that adapt according to the vehicle's response in all flight regimes. To validate this controller, numerical simulations in Matlab and flight tests were conducted. The combination of these validation methods confirms our adaptive controller's ability to control the transition between the vertical and horizontal flight regimes when faced with both parametric uncertainties and external disturbances. / Master of Science / Unmanned aircrafts have been a topic of constant research and development recently due to their wide range of applications and their ability to fly without directly involving pilots. More specifically, VTOL UAVs have the advantage of being able to take off without a runway while retaining the efficiency of a classical aircraft. A tailsitter UAV behaves as a traditional quadrotor drone when in its vertical configuration and can rotate to a horizontal configuration, where it takes advantage of its wings to fly as a conventional aircraft. Modeling the dynamics of the tailsitter UAV and designing an autopilot controller is the main focus of this thesis. An adaptive controller was chosen for the tailsitter UAV due to its ability to modify the gains of the system based on the behavior of the vehicle to adapt to the unknown vehicle properties. This controller was validated using both computer simulations and actual flight tests. It was found that the adaptive controller was able to successfully control the transition between the vertical and horizontal flight regimes despite the uncertainties in the parameters of the vehicle.

In this dissertation, new model reference adaptive control architectures are presented with stability, performance, and robustness considerations, to address challenges related to the verification of adaptive control systems. The challenges associated with the transient performance of adaptive control systems is first addressed using two new approaches that improve the transient performance. Specifically, the first approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimization procedure to minimize the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. The second approach is an extension of the first one and minimizes the effect of the system uncertainties more directly in the transient phase. In addition, this approach uses a varying gain to enforce performance bounds on the system error and is further generalized to adaptive control laws with nonlinear reference models. Another challenge in adaptive control systems is to achieve system stability and a prescribed level performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. Another major contribution of this dissertation is to address this challenge. In particular, first a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability limits of this approach are computed using linear matrix inequalities revealing the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, these computations are used to provide a depiction of the feasible region of the actuator parameters such that the robustness to variation in the parameters is addressed. Furthermore, the convergence properties of the modified reference model to the ideal reference model are analyzed. Generalizations and applications of the proposed approach are then provided. Finally, to improve upon this linear matrix inequalities-based hedging approach a new adaptive control architecture using expanded reference models is proposed. It is shown that the expanded reference model trajectories more closely follow the trajectories of the ideal reference model as compared to the hedging approach and through the augmentation of a command governor architecture, asymptotic convergence to the ideal reference model can be guaranteed. To provide additional robustness against possible uncertainties in the actuator bandwidths an estimation of the actuator bandwidths is incorporated. Lastly, the challenge presented by the unknown physical interconnection of large-scale modular systems is addressed. First a decentralized adaptive architecture is proposed in an active-passive modular framework. Specifically, this architecture is based on a set-theoretic model reference adaptive control approach that allows for command following of the active module in the presence of module-level system uncertainties and unknown physical interconnections between both active and passive modules. The key feature of this framework allows the system error trajectories of the active modules to be contained within apriori, user-defined compact sets, thereby enforcing strict performance guarantees. This architecture is then extended such that performance guarantees are enforced on not only the actuated portion (active module) of the interconnected dynamics but also the unactuated portion (passive module). For each proposed adaptive control architecture, a system theoretic approach is included to analyze the closed-loop stability properties using tools from Lyapunov stability, linear matrix inequalities, and matrix mathematics. Finally, illustrative numerical examples are included to elucidate the proposed approaches.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

The objective of adaptive control is to design a controller that can adjust its behaviour to tolerate uncertain or time-varying parameters. An adaptive controller typically consists of a linear time-invariant (LTI) compensator together with a tuning mechanism which adjusts the compensator parameters and yields a nonlinear controller. Because of the nonlinearity, the transient closed-loop behaviour is often poor and the control signal may become unduly large. Although the initial objective of adaptive control was to deal with time-varying plant parameters, most classical adaptive controllers cannot handle rapidly changing parameters. Recently, the use of a linear periodic (LP) controller has been proposed as a new approach in the field of model reference adaptive control [1]. In this new approach, instead of estimating plant parameters, the “ideal control signal” (what the control signal would be if the plant parameters and states were measurable) is estimated. The resulting controller has a number of desirable features: (1) it handles rapid changes in the plant parameters, (2) it provides nice transient behaviour of the closed-loop system, (3) it guarantees that the effect of the initial conditions declines to zero exponentially, and (4) it generates control signals which are modest in size. Although the linear periodic controller (LPC) has the above advantages, it has some imperfections. In order to achieve the desirable features, a rapidly varying control signal and a small sampling period are used. The rapidly time-varying control signal requires fast actuators which may not be practical. The second weakness of the LPC [1] is poor noise rejection behaviour. The small sampling period results in large controller gains and correspondingly poor noise sensitivity, since there is a clear trade-off between tracking and noise tolerance. As the last drawback, this controller requires knowledge of the exact plant relative degree. Here we extend this work in several directions: (i) In [1], the infinity-norm is used to measure the signal size. Here we redesign the controller to yield a new version which provides comparable results when the more common 2-norm is used to measure signal size, (ii) A key drawback of the controller of [1] is that the control signal moves rapidly. Here we redesign the control law to significantly alleviate this problem, (iii) The redesigned controller can handle large parameter variation and in the case that the sign of high frequency gain is known, the closed-loop system is remarkably noise-tolerant, (iv) We prove that in an important special case, we can replace the requirement of knowledge of the exact relative degree with that of an upper bound on the relative degree, at least from the point of view of providing stability, and (v) A number of approaches to improve the noise behaviour of the controller are presented. Reference: [1] D. E. Miller, “A New Approach to Model Reference Adaptive Control”, IEEE Transaction on Automatic Control, Vol. 48, No. 5, pages 743-756, May 2003.

A simple design methodology of optimal model reference adaptive control (OMRAC) scheme with perturbation estimation for solving robust tracking problems is proposed in this thesis. The plant to be controlled belongs to a class of MIMO perturbed dynamic systems with input nonlinearity and time varying delay. The proposed robust tracking controller with a perturbation estimation scheme embedded is designed by using Lyapunov stability theorem. The control scheme contains three types of controllers. The first one is a linear feedback optimal controller, which is designed under the condition that no perturbation exists. The second one is an adaptive controller, it is used for adapting the unknown upper bound of perturbation estimation error. The third one is the perturbation estimation mechanism. The property of uniformly ultimately boundness is proved under the proposed control scheme, and the effects of each design parameter on the dynamic performance is also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.

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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