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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.

Human expert drivers have the unique ability to build complex perceptive models using correlated sensory inputs and outputs. In the case of longitudinal vehicle traction, this work will show a direct correlation in longitudinal acceleration to throttle input in a controlled laboratory environment. In fact, human experts have the ability to control a vehicle at or near the performance limits, with respect to vehicle traction, without direct knowledge of the vehicle states; speed, slip or tractive force. Traditional algorithms such as PID, full state feedback, and even sliding mode control have been very successful at handling low level tasks where the physics of the dynamic system are known and stationary. The ability to learn and adapt to changing environmental conditions, as well as develop perceptive models based on stimulus-response data, provides expert human drivers with significant advantages. When it comes to bandwidth, accuracy, and repeatability, automatic control systems have clear advantages over humans; however, most high performance control systems lack many of the unique abilities of a human expert. The underlying motivation for this work is that there are advantages to framing the traction control problem in a manner that more closely resembles how a human expert drives a vehicle. The fundamental idea is the belief that humans have a unique ability to adapt to uncertain environments that are both temporal and spatially varying. In this work, a novel approach to traction control is developed using an anthropomimetic control synthesis strategy. The proposed anthropomimetic traction control algorithm operates on the same correlated input signals that a human expert driver would in order to maximize traction. A gradient ascent approach is at the heart of the proposed anthropomimetic control algorithm, and a real-time implementation is described using linear operator techniques, even though the tire-ground interface is highly non-linear. Performance of the proposed anthropomimetic traction control algorithm is demonstrated using both a longitudinal traction case study and a combined mode traction case study, in which longitudinal and lateral accelerations are maximized simultaneously. The approach presented in this research should be considered as a first step in the development of a truly anthropomimetic solution, where an advanced control algorithm has been designed to be responsive to the same limited input signals that a human expert would rely on, with the objective of maximizing traction. This work establishes the foundation for a general framework for an anthropomimetic control algorithm that is capable of learning and adapting to an uncertain, time varying environment. The algorithms developed in this work are well suited for efficient real time control in ground vehicles in a variety of applications from a driver assist technology to fully autonomous applications. / Ph. D.

The presented research concerns the control of unmanned vehicles. The results introduced in this dissertation provide a solid control framework for a wide class of nonlinear uncertain systems, with a special emphasis on issues related to implementation, such as control input amplitude and rate saturation, or partial state measurements availability. More specifically, an adaptive control framework, allowing to enforce amplitude and rate saturation of the command, is developed. The motion control component of this framework, which works in conjunction with a saturation algorithm, is then specialized to different types of vehicles. Vertical take-off and landing aerial vehicles and a general class of autonomous marine vehicles are considered. A nonlinear control algorithm addressing the tracking problem for a class of underactuated, non-minimum phase marine vehicles is then introduced. This motion controller is extended, using direct and indirect adaptive techniques, to handle parametric uncertainties in the system model. Numerical simulations are used to illustrate the efficacy of the algorithms. Next, the output feedback control problem is treated, for a large class of nonlinear and uncertain systems. The proposed solution relies on a novel nonlinear observer which uses output measurements and partial knowledge of the system's dynamics to reconstruct the entire state for a wide class of nonlinear systems. The observer is then extended to operate in conjunction with a full state feedback control law and solve both the output feedback control problem and the state observation problem simultaneously. The resulting output feedback control algorithm is then adjusted to provide a high level of robustness to both parametric and structural model uncertainties. Finally, in a natural extension of these results from motion control of a single system to collaborative control of a group of vehicles, a cooperative control framework addressing limited communication issues is introduced. / Ph. D.

The author proposes a novel functional regression method for parameter estimation and adaptive control in this dissertation. In the functional regression method, the regressors and a signal which contains the information of the unknown parameters are either determined from raw measurements or calculated as the functions of the measurements. The novel feature of the method is that the algorithm maps the regressors to the functionals which are represented in terms of customized test functions. The functionals are updated continuously by the evolution laws, and only an infinite number of variables are needed to compute the functionals. These functionals are organized as the entries of a matrix, and the parameter estimates are obtained using either the generalized inverse method or the transpose method. It is shown that the schemes of some conventional adaptive methods are recaptured if certain test function designs are employed. It is proved that the functional regression method guarantees asymptotic convergence of the parameter estimation error to the origin, if the system is persistently excited. More importantly, in contrast to the conventional schemes, the parameter estimation error may be expected to converge to the origin even when the system is not persistently excited. The novel adaptive method are also applied to the Model Reference Adaptive Controller (MRAC) and adaptive observer. It is shown that the functional regression method ensures asymptotic stability of the closed loop systems. Additionally, the studies indicate that the transient performance of the closed loop systems is improved compared to that of the schemes using the conventional adaptive methods. Besides, it is possible to analyze the transient responses a priori of the closed loop systems with the functional regression method. The simulations verify the theoretical analyses and exhibit the improved transient and steady state performances of the closed loop systems. / Ph. D.

The design of nonlinear adaptive control systems for reducing vibration transmission in applications such as transportation systems is discussed. The systems studied include suspension systems, such as those used in vehicles, employing nonlinear magneto-rheological (MR) dampers that are controlled to provide improved vibration isolation. Magneto-rheological dampers use a novel class of smart fluid whose apparent viscosity changes as it is exposed to a magnetic field. The developed adaptive control scheme is designed to deal with the nonlinearities and uncertainties that commonly arise in most suspension applications. Some of the nonlinearities that are considered include time-varying characteristics, displacement-dependent effects, and hysterisis damping of magneto-rheological dampers. The uncertainties include mass and stiffness variations that can commonly occur in a suspension system. A number of nonlinear analytical models are developed and used in numerical simulation to evaluate the validity and effectiveness of the developed adaptive controllers. Further, the results of the numerical study are used in an experimental evaluation of the controllers on a seat suspension for heavy vehicles. The analytical and experimental evaluation both indicate the effectiveness of the proposed adaptive control technique in controlling vibration transmission in the presence of both system nonlinearities and uncertainties. The manuscript will provide a detail account of the modeling, dynamic analysis, adaptive control development, and testing that was performed throughout this study. / Ph. D.

In this dissertation, guidance and control of autonomous unmanned aerial systems (UAS) are explored. Specifically, we investigate model reference adaptive control (MRAC) based systems for tailsitter UAS, and guidance and control of multi-rotor UAS for tactical maneuvering and coverage. Applications, both current and potential, are investigated and gaps in existing technologies are identified. To address the controls problem of a particular class of tailsitter UAS, that is, quadrotor-biplanes, subject to modeling uncertainties, unmodeled payloads, wind gusts, and actuator faults and failures, two approaches are developed. In the first approach, the longitudinal dynamics of a tailsitter UAS are regulated using an MRAC law for prescribed performance and output tracking in a novel control architecture. The MRAC law for prescribed performance and output tracking incorporates a Linear Quadratic Regulator (LQR) baseline controller using integral-feedback interconnections. Constraints on the trajectory tracking error are enforced using barrier Lyapunov functions, and a user-defined rate of convergence of the trajectory tracking error is guaranteed by employing a reference model for the trajectory tracking error's transient dynamics. In this control system, the translational and rotational dynamics are split into an outer loop and an inner loop, respectively, to account for the underactuation of the quadrotor-biplane. In the outer loop, estimates of the aerodynamic forces and MRAC laws are used to stabilize the translational dynamics. Furthermore, the reference pitch angle is deduced such that the vehicle's total thrust never points towards the Earth for safety, and discontinuities inherent to the signed arctangent function commonly used for determining orientations are avoided. In the inner loop, estimates of the aerodynamic moment and an MRAC law are used to stabilize the rotational dynamics. A law for determining the desired total thrust is proposed, which ensures that if the vehicle's orientation is close enough to the desired orientation, then the proper thrust force is applied. A control allocation scheme is presented to ensure that the desired moment of the thrust force is always realized, and constraints on the non-negativity of the thrust force produced by the actuators are satisfied. The proposed control architecture employing MRAC for prescribed performance and output signal tracking is validated in simulation, and the MRAC law for prescribed performance is compared to the classical MRAC law. In the second approach, a unified control architecture based on MRAC is presented which does not separate the longitudinal and lateral-directional dynamics. The translational and rotational dynamics are separated into outer and inner loops, respectively, to address the underactuation of the tailsitter UAS. Since it is expected that the vehicle will undergo large rotations, the tailsitter's orientation is captured using quaternions, which are singularity-free. Furthermore, the windup phenomenon is addressed by employing barrier Lyapunov functions to ensure that the first component of the tracking error quaternion is positive, and thus, the shortest rotation is followed to drive the vehicle's current orientation to the reference orientation. In the outer loop, the desired thrust force is determined using estimates of the aerodynamic forces and an MRAC law. The reference orientation is determined as a solution of the orthogonal Procrustes' problem, which finds the smallest rotation from the current orientation of the thrust force, to the orientation of th desired thrust force. The angular velocity and acceleration cannot be deduced by taking the time derivative of the solution of the orthogonal Procrustes' problem due to the discontinuous nature of the singular value decomposition. Therefore, the twice continuously differentiable function, spherical linear interpolation, is used to find a geodesic joining the unit quaternion capturing the vehicle's current orientation, and the unit quaternion capturing the reference orientation. An interesting result is that the angular velocity and acceleration depend only on the first and second derivatives of the scalar-valued function which parameterizes the spherical linear interpolation function; the actual function is immaterial. However, determining the shape of this function is nontrivial, and hence, an approach inspired by model predictive control is used. In the inner loop, estimates of the aerodynamic moment and an MRAC law are used to stabilize the rotational dynamics, and the thrust force is allocated to the individual propellers. The validity of the proposed control scheme is presented in simulation. An integrated guidance and control system for autonomous UAS is proposed to maneuver in an unknown, dynamic, and potentially hostile environment in a reckless or tactical manner as prescribed by the user. Tactical maneuvering in this guidance and control system is enabled through exploitation of obstacles in the environment for shelter as the vehicle approaches its goal. Reckless maneuvering is enabled by ignoring the presence of nearby obstacles while proceeding towards the goal, while remaining collision-free. The demarcation of reckless and tactical behaviors are bio-inspired, since these tactics are used by animals or ground-based troops. The guidance system fuses a path planner, collision-avoidance algorithm, vision-based navigation system, and a trajectory planner. The path planner is based on the A* search algorithm, and a custom tunable cost-to-come and heuristic function are proposed to enable the exploitation of the obstacles' set for shelter by decreasing the weight of edges in the underlying graph that capture nodes close to the obstacles' set. The consistency of the heuristic is established, and hence, the search algorithm will return an optimal solution, and not expand nodes multiple times. In realistic scenarios, fast replanning is necessary to ensure that the system realizes the desired behavior, and does not collide with obstacles. The trajectory planner is based on fast model predictive control (fMPC), and thus, can be executed in real time. A custom tunable cost function, which weighs the importance of proximity to the obstacles' set and proximity to the goal, is employed to provide another mechanism for enabling tactical behaviors. The novel collision avoidance algorithm is based on the solution of a particular class of semidefinite programming problems, that is, quadratic discrimination. The collision avoidance algorithm produces convex sets of free space near the UAS by finding ellipsoids that separate the UAS from the obstacles' set. The convex sets are used in the fMPC framework as inequality constraints. The collision avoidance algorithm's computational burden is determined empirically, and is shown to be faster than two similar algorithms in the literature. The modules above are integrated into a single guidance system, which supplies reference trajectories to an arbitrary control system, and the validity of the proposed approach is exhibited in several simulations and flight tests. Furthermore, a taxonomy of flight behaviors is presented to understand how the tunable parameters affect the recklessness or stealthiness of the resulting trajectory. Lastly, an integrated guidance and control system for autonomous UAS performing tactical coverage in an unknown, dynamic, and potentially hostile environment in a reckless or tactical manner as prescribed by the user is presented. The guidance problem for coverage concerns strategies and route planning for gathering information about an environment. The aim of gathering information about an unknown environment is to aid in situational awareness and planning for service organizations and first-responders. To address this problem, goal selection, path planning, collision avoidance, and trajectory planning are integrated. A novel goal selection algorithm based on the Octree data structure is proposed to autonomously determine goal points for the path planner. In this algorithm, voxel maps deduced by a navigation system, which capture the occupancy and exploration status of areas of the environment, are segmented into partitions that capture large unexplored areas, and large explored areas. Large unexplored areas are used as candidates for goal points. The feasibility of goal points is determined by employing a greedy $A^*$ technique. The algorithm boasts tunable parameters that allow the user to specify a greedy or systematic behavior when determining a sequence of goal points. The computational burden of this technique is determined empirically, and is shown to be useful for real-time use in realistic scenarios. The path planner is based on the Lifelong Planning $A^*$ ($LPA^*$) search algorithm which is shown to have advantages over the $A^*$ technique. A custom tunable cost-to-come and heuristic function are proposed to enable tactical or reckless path planning. A novel collision avoidance algorithm is proposed as an improved version of the aforementioned collision avoidance algorithm, where the volume of the resulting constraint sets are improved, and thus, more of the free space is captured by the convex set, and hence, the trajectory planner can exploit more of the environment for tactical maneuvering. This algorithm is based on semidefinite programming and a fast approximate convex hull algorithm. The trajectory planner is based on fMPC, employs a custom cost function to enable tactical maneuvering by coasting the surface of obstacles and regulation of the desired acceleration as a function of proximity to shelter, employs barrier functions to constrain the attitude of the vehicle and ensure thrust positivity, and employs a quadrotor UAS' output feedback linearized equations of motion as differential constraints to enable aggressive maneuvering. The efficacy of the proposed system is validated using a custom-made C++ simulator. / Doctor of Philosophy / In recent years, unmanned aerial systems (UAS) such as quadcopters, hexacopters, and octocopters, have seen increased popularity for a myriad of applications including crop monitoring, photography, surveying, surveillance, wireless network extension, search and rescue, firefighter support, and military operations, to name a few. This list of applications stems from UAS' maneuverability, adaptability, accessibility, and their absence of an onboard pilot. While some of these applications can be executed with current capabilities, the performance of these systems could be improved, and there are many applications where UAS could be used to fulfil substantial roles in areas such as logistics, tactical surveillance, and direct human-interaction. However, these applications require a considerable improvement in autopilot design for UAS; shortcomings of current capabilities are identified in this thesis. Indeed, one of the most important improvements to be made is enabling fully autonomous operations where limited human intervention and oversight is necessary for mission success. In this thesis, we present two adaptive control systems for tailsitter UAS to enable accurate trajectory tracking in realistic scenarios with degraded conditions, such as inclement weather with unsteady winds, poorly-modeled dynamics as a result of negligence or a cost-benefit analysis, failing actuators due to overuse or damage from collisions. In the first adaptive control system, we focus on the tailsitter UAS' longitudinal dynamics, and employ a novel adaptive control technique to stabilize the system. In the second adaptive control system, we do not separate the longitudinal and lateral-directional dynamics, and split the tailsitter UAS' translational and rotational dynamics into outer and inner loops, respectively. In this control system, the windup problem is addressed using barrier functions, the reference orientation is determined as a solution to the orthogonal Procrustes' problem, and the system's dynamics are stabilized using model reference adaptive control. Furthermore, in this dissertation, we develop and present a guidance and control system which can be used to enable autonomous intelligence, surveillance, reconnaissance, and logistics (ISRL) operations in unknown, dynamic, and potentially hostile environments. The guidance system enables the UAS to achieve a user-defined behavior which ranges from tactical to reckless. The tactical or reckless behaviors are enabled through the guidance system's path planner, which is based on the A* search algorithm employing custom cost and heuristic function. Similarly, the guidance system's trajectory planner, which is based on fast model predictive control (fMPC), enables tactical or reckless behaviors through a custom cost function. The problem of collision-avoidance is handled through the path planner, which returns collision-free paths, and a novel constraint set generation algorithm which deduces regions of free space near the UAS; these regions are used as constraint sets for the trajectory planner. We validate the proposed approach in simulation and flight tests, and present a taxonomy of flight behaviors.

This dissertation is concerned with the development of two adaptive state estimators that are capable of tracking linear plants that undergo rapid configuration changes. The first is a modification of the Partitioned Adaptive Estimator, PAE, first introduced by Magill in 1965, improved and named by Lainiotis, and used in a number of applications, primarily aerospace. The PAE algorithm was derived for the problem of identifying which, of N, configurations that a linear plant is in; the key assumption being that the configuration is unknown but unchanging. There are two main difficulties in extending the PAE algorithm to the problem of estimating the state of a linear plant that can undergo configuration changes (the switched-linear plant problem). These two difficulties are addressed and solved in this dissertation. The result is called the modified PAE algorithm. The second adaptive estimator developed in this dissertation is the "Sliding Window Detector/Estimator” or SWDE algorithm. Unlike the modified PAE algorithm whose basic structure is designed to solve a different problem, the SWDE algorithm is designed specifically for the switched-linear plant problem. It uses a joint detection/estimation approach to give a very close approximation to the unrealizable optimum switched-linear estimator. The advantages and disadvantages of the two adaptive estimators are discussed, and it is found that a very reliable and accurate estimator can be constructed by combining both algorithms. Several different examples are given to clarify the operation of the estimator. A second contribution of this dissertation is in the application of the above estimators to the nonlinear estimation problem. The motivation for this approach is that a nonlinear plant can be approximated by a sequence of linear approximations, or configurations. Thus, an estimator that works for a switched-linear plant can perform as a sub-optimum nonlinear estimator. In addition, a stochastic nonlinear controller can be constructed using the nonlinear estimator as the observer. This approach has several significant implementation and design advantages which are discussed in the dissertation and illustrated by two examples, a set-point control example and a trajectory-following aircraft example. The above examples and algorithms were fully verified by extensive computer simulation. The implementation advantages afforded by these methods make them practical in a wide variety of applications. / Ph. D.

During the past decade, researchers have shown much interest in control and identification of Large Space Structures (LSS). Our inability to model these LSS accurately has generated extensive research into robust controllers capable of maintaining stability in the presence of large structural uncertainties as well as changing structural characteristics. In this work the performance of Model Reference Adaptive Control - (MRAC) is studied in numerical simulations and verified experimentally, to understand how differences between the plant and the reference model affect the control effort. MRAC is applied analytically and experimentally to a single-degree-of-freedom system and analytically to a multi-degree-of-freedom system with multi-inputs and multi-outputs. Good experimental and analytical agreement is demonstrated in control experiments and it is shown that MRAC does an excellent job of controlling the structures and achieving the desired performance even when large differences between the plant and ideal reference model exist. However, it is shown that reasonable differences between the reference model and the plant significantly increase the required control effort. The effects of increased damping in the reference model are considered, and it is shown that requiring the controller to provide increased damping actually decreases the required control effort when differences between the plant and reference model exist. This result is very useful because one of the first attempts to counteract the increased control effort due to differences between the plant and reference model might be to require less damping, however, this would actually increase the control effort. The use of optimization to successfully improve performance and reduce control effort is shown to be limited, because the actual control-structure system can not realize all the performance improvements of the analytical optimal system. Finally, it is shown that very large sampling rates may be required to accurately implement MRAC. / Ph. D.

The first and most imperative step when designing a biologically inspired robot is to identify the underlying mechanics of the system or animal of interest. It is most common, perhaps, that this process generates a set of coupled nonlinear ordinary or partial differential equations. For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. This is particularly true if joint and link flexibility are included in the model. In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics of animal motion are very hard to model. A very well-established example of these forces is the unsteady aerodynamic forces applied to the wings and the body of insects, birds, and bats. These forces result from the interaction of the flapping motion of the wing and the surround- ing air. These forces generate lift and drag during flapping flight regime. As a result, they play a significant role in the description of the physics that underlies such systems. In this research we focus on dynamic and kinematic models that govern the motion of ground based robots that emulate flapping flight. The restriction to ground based biologically inspired robotic systems is predicated on two observations. First, it has become increasingly popular to design and fabricate bio-inspired robots for wind tunnel studies. Second, by restricting the robotic systems to be anchored in an inertial frame, the robotic equations of motion are well understood, and we can focus attention on flapping wing aerodynamics for such nonlinear systems. We study nonlinear modeling, identification, and control problems that feature the above complexities. This document summarizes research progress and plans that focuses on two key aspects of modeling, identification, and control of nonlinear dynamics associated with flapping flight. / Ph. D.