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.

This dissertation explores a novel omnidirectional propulsion mechanism for observation-class underwater vehicles, enabling for operation in extreme, hostile, or otherwise high-speed turbulent environments where unprecedented speed and agility are necessary. With a small overall profile, the mechanism consists of two sets of counter-rotating blades operating at frequencies high enough to dampen vibrational effects on onboard sensors. Each rotor is individually powered to allow for roll control via relative motor effort and attached to a swashplate mechanism, providing quick and powerful manipulation of fluid-flow direction in the hull's coordinate frame without the need to track rotor position. The omnidirectional mechanism exploits properties emerging from its continuous counter-rotating blades to generate near-instantaneous forces and moments in six degrees of freedom (DOF) of considerable magnitude, and is designed to allow each DOF to be controlled independently by one of six decoupled control parameters. The work presented in this dissertation validates the mechanism through physical small-scale experimentation, confirming near-instantaneous reaction time, and aligning with computational fluid dynamic (CFD) results presented for the proposed theorized full-scale implementation. Specifically, it is demonstrated that the mechanism can generate sway thrust at 10-20% surge thrust capacity in both simulation and physical tests. It is also shown that the magnitude of forces and moments generated is directly proportional to motor effort and corresponding commands, in par with theory. Any apparent couplings between different control modes are deeply understood and shown to be trivially accounted for, effectively uncoupling all six control parameters. The design, principles, and bullard-pull simulation of the proposed full-scale mechanism and vehicle implementation are then thoroughly discussed. Kinematic and hydrodynamic analyses of the hull and surrounding fluid forces during different maneuvers are presented, followed by the mechanical design and kinematic analysis of each subsystem. To estimate proposed full-scale performance specifications and UUV turbulence rejection, a full six-DOF maneuvering model is constructed from first principles utilizing CFD and regression techniques. This dissertation thoroughly examines the working principles and performance of a novel omnidirectional propulsion mechanism. With the small-scale model and full scale simulation and analysis, the work presented successfully demonstrates the mechanism can generate nearly instantaneous omnidirectional forces underwater in a controlled manner, with application to high-speed agile vehicles in dynamic environments. / Doctor of Philosophy / This dissertation explores a novel omnidirectional propulsion mechanism for observation-class underwater vehicles, enabling for operation in extreme, hostile, or otherwise high-speed turbulent environments where unprecedented speed and agility are necessary. The mechanism utilizes independently-powered rotors to command near-instantaneous forces and moments in all six degrees of freedom (DOF). The design allows each DOF to be independently controlled by one of six decoupled control parameters. The method for generating lateral thrust through the mechanism is originally verified through computational fluid dynamic (CFD) tests, but the complete novelty of the lateral maneuver calls for physical verification for any noteworthy validation. The work presented in this dissertation validates the mechanism through physical small-scale experimentation, confirming near-instantaneous reaction time, and aligning with CFD results presented for the proposed theorized full-scale implementation. Specifically, it is demonstrated that the mechanism can generate sway (side/side) thrust at 10-20% surge (forward/backward) thrust capacity in both simulation and physical tests. It is also shown that the magnitude of forces and moments generated is directly proportional to motor effort and corresponding commands, in par with theory. Finally, a full six-DOF model for underwater vehicle trajectory is constructed utilizing detailed maneuvering techniques to estimate full-scale performance. With the small-scale model and full-scale simulation and analysis, the work successfully demonstrates the mechanism can generate nearly instantaneous omnidirectional forces underwater in a controlled manner, with application to high-speed agile vehicles in dynamic environments.

M.S.

A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters. / Master of Science

This dissertation focuses on problems in design, optimization and control of complex, large-scale dynamical systems from different viewpoints. The goal is to develop new algorithms and methods, that solve real problems more efficiently, together with providing mathematical insight into the success of those methods. There are three main contributions in this dissertation. In Chapter 3, we provide a new method to solve large-scale algebraic Riccati equations, which arise in optimal control, filtering and model reduction. We present a projection based algorithm utilizing proper orthogonal decomposition, which is demonstrated to produce highly accurate solutions at low rank. The method is parallelizable, easy to implement for practitioners, and is a first step towards a matrix free approach to solve AREs. Numerical examples for n >= 100,000 unknowns are presented. In Chapter 4, we develop a system identification method which is motivated by tangential interpolation. This addresses the challenge of fitting linear time invariant systems to input-output responses of complex dynamics, where the number of inputs and outputs is relatively large. The method reduces the computational burden imposed by a full singular value decomposition, by carefully choosing directions on which to project the impulse response prior to assembly of the Hankel matrix. The identification and model reduction step follows from the eigensystem realization algorithm. We present three numerical examples, a mass spring damper system, a heat transfer problem, and a fluid dynamics system. We obtain error bounds and stability results for this method. Chapter 5 deals with control and observation design for parameter dependent dynamical systems. We address this by using local parametric reduced order models, which can be used online. Data available from simulations of the system at various configurations (parameters, boundary conditions) is used to extract a sparse basis to represent the dynamics (via dynamic mode decomposition). Subsequently, a new compressed sensing based classification algorithm is developed which incorporates the extracted dynamic information into the sensing basis. We show that this augmented classification basis makes the method more robust to noise, and results in superior identification of the correct parameter. Numerical examples consist of a Navier-Stokes, as well as a Boussinesq flow application. / Ph. D.

This research presents an investigation into the development of real time system identification using intelligent algorithms. A simulation platform of a flexible beam vibration using finite difference (FD) method is used to demonstrate the real time capabilities of the identification algorithms. A number of approaches and algorithms for on line system identifications are explored and evaluated to demonstrate the merits of the algorithms for real time implementation. These approaches include identification using (a) traditional recursive least square (RLS) filter, (b) Genetic Algorithms (GAs) and (c) adaptive Neuro_Fuzzy (ANFIS) model. The above algorithms are used to estimate a linear discrete second order model for the flexible beam vibration. The model is implemented, tested and validated to evaluate and demonstrate the merits of the algorithms for real time system identification. Finally, a comparative performance of error convergence and real time computational complexity of the algorithms is presented and discussed through a set of experiments.

<p dir="ltr">The research presents the structure and a prototype an innovative parallel robotic structure using 3 mobile bases for actuation and hybrid motion. A system identification was performed to verify the model of the robot.</p>

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.

The modern day power grid is a highly complex system; as such, maintaining stable operations of the grid relies on many factors. Additionally, the increased usage of renewable energy sources significantly complicates matters. Attempts to assess the current stability of the grid make use of several key parameters, however obtaining these parameters to make an assessment has its own challenges. Due to the limited number of measurements and the unavailability of information, it is often difficult to accurately know the current value of these parameters needed for stability assessment. This work attempts to estimate three of these parameters: the Inertia, Topology, and Voltage Phasors. Without these parameters, it is no longer possible to determine the current stability of the grid. Through the use of machine learning, empirical studies, and mathematical optimization it is possible to estimate these three parameters when previously this was not the case. These three methodologies perform estimations through measurement-based approaches. This allows for the obtaining of these parameters without required system knowledge, while improving results when systems information is known. / Ph. D.

The purpose of this study has two parts directed toward a common goal. First, a state-ofthe-art quarter-car test platform has been designed and constructed to offer increased testing flexibility at a reasonable cost not found commercially. With this new test rig completed, the second objective is a proof-of-concept evaluation of a well known adaptive control algorithm applied to this new quarter-car test rig for the purpose of replicating the dynamic suspension response, such as a response that was recorded during a road test. A successful application of this control algorithm on the quarter-car rig is the necessary first step toward its application on an 8-post test rig for a direct comparison to current practices. Before developing a new test rig, the current state-of-the-art in quarter-car rigs was first evaluated as well as indoor vehicle testing in general. Based on these findings, a list of desired functional requirements was defined for this new design to achieve. The new test rig was built and evaluated to determine how these goals were met and what the next steps would be to improve the rig. The study then focused on evaluating control policies used for reproducing dynamic responses on vehicle road simulators such as 4- post and 7-post shaker rigs. A least-mean squares (LMS) adaptive algorithm is introduced and applied first in software using a linear two-mass quarter-car model, and then to the actual hardware-in-the-loop quarter-car rig. The results of the study show that the resulting quarter-car test rig design is quite flexible in its ability to test a multitude of suspension designs and also its ability to accommodate new hardware in the future such as a body loaders. The study confirms that this particular implementation of the LMS algorithm is a viable option for replicating test vehicle response on an indoor quarter-car test rig. Thus, a future study to compare the use of this algorithm to the current industry standard batch processing method is possible. / Master of Science