Circadian rhythms exist in almost all of living species, and they occupy an important role in daily biological activities of these species. This thesis deals with reduction of measurements in circadian models, and recovery of circadian phases. Two mathematical models of circadian rhythms are considered, with a 3rd order model for Neurospora, and a 7th order model for Mammals. The reduction of measurements of circadian models is shown by the proposals of observer designs to the two mathematical models of circadian rhythms. Both mathematical models contain strong nonlinearities, which make the observer design challenging. Two observer designs, reduced-order and one-sided Lipschitz, are applied to the circadian models to tackle the nonlinearities. Reduced-order observer design is based on a state transformation to make certain nonlinearities have no impact on the observer errors, and the design of one-sided Lipschitz observer is based on systems with one-sided Lipschitz nonlinearities. Both observer designs are based on the existing methods in literature. The existing method of reduced-order observer has been applied to a class of multi-output nonlinear systems. A new reduced-order observer design which extends the existing one in literature is presented in this thesis. In this new reduced-order observer method, the observer error dynamics can be designed by choosing the observer gain, unlike the existing one, of which the observer error dynamics depend on the invariant zeros under certain input-output map. The recovery of circadian phases is carried out to provide a solution to phase shifts occurred in circadian disorders. The restoration of circadian phases is performed by the synchronizations of trajectories of a controlled model with trajectories of a reference model. The reference model and the controlled model have phase differences, and both these models are based on a given 3rd order model of Neurospora circadian rhythms. The phase differences are reflected by different initial conditions, and by parameter uncertainty. The synchronizations of the two models are performed by using back-stepping method for the case of different initial conditions, and by using adaptive back-stepping method for the remaining case. Several simulation studies of the proposed observer designs and the proposed schemes of synchronizations are carried out with the results shown in this thesis.

The study of fixed wing aeronautical engineering has matured to the point where years of research result in small performance improvements.  In the past decade, micro air vehicles, or MAVs, have gained attention of the aerospace and robotics communities.  Many researchers have begun investigating aircraft schemes such as ones which use rotary or flapping wings for propulsion.  While the engineering of rotary wing aircraft has seen significant advancement, the complex physics behind flapping wing aircraft remains to be fully understood.  Some studies suggest flapping wing aircraft can be more efficient when the aircraft operates in low Reynolds regimes or requires hovering.  Because of this inherent complexity, the derivation of flapping wing control methodologies remains an area with many open research problems.  This thesis investigates flapping wing vehicles whose design is inspired by avian flight.  The flapping wing system is examined in the cases where the core body is fixed or free in the ground frame.  When the core body is fixed, the Denavit Hartenberg representation is used for the kinematic variables.  An alternative approach is introduced for a free base body case.  The equations of motion are developed using Lagranges equations and a process is developed to derive the aerodynamic contributions using a virtual work principle.  The aerodynamics are modeled using a quasi-steady state formulation where the lift and drag coefficients are treated as unknowns.  A collection of nonlinear controllers are studied, specifically an ideal dynamic inversion controller and two switching dynamic inversion controllers.  A dynamic inversion controller is modified with an adaptive term that learns the aerodynamic effects on the equation of motion.  The dissipative controller with adaptation is developed to improve performance.  A Lyapunov analysis of the two adaptive controllers guarantees boundedness for all error terms.  Asymptotic stability is guaranteed for the derivative error in the dynamic inversion controller and for both the position and derivative error in the dissipative controller.  The controllers are simulated using two dynamic models based on flapping wing prototypes designed at Virginia Tech.  The numerical experiments validate the Lyapunov analysis and illustrate that unknown parameters can be learned if persistently excited. / Master of Science

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The rising levels of autonomy exhibited by complex cyber-physical systems have brought questions related to safety and adaptation to the forefront of the minds of controls and robotics engineers. Often, such autonomous systems are deemed to be safety-critical in the sense that failures during operation could significantly harm the system itself, other autonomous systems, or, in the worst-case, humans interacting with such a system. Complicating the design of control and decision-making algorithms for safety-critical systems is that they must cope with various degrees of uncertainty as they are deployed autonomously in increasingly real-world environments. These challenges motivate the use of learning-based techniques that can adapt to such uncertainties while adhering to safety-critical constraints. The main objective of this dissertation is to present a unified framework for the design of controllers that learn from data online with formal guarantees of safety. Rather than using a controller trained on an a priori dataset collected offline that is then statically deployed on a system, we are interested in using real-time data to continuously update the control policy online and cope with uncertainties that are challenging to characterize until deployment. We approach the problem of designing such learning-based control algorithms for safety-critical systems through the use of certificate functions, such as Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs), from nonlinear control theory. To this end, we first discuss how modern data-driven techniques can be integrated into traditional adaptive control frameworks to develop classes of CLFs and CBFs that facilitate the design of both controllers and learning algorithms that guarantee, respectively, stability and safety by construction. Next, we shift from the problem of safe adaptive control to safe reinforcement learning where we demonstrate how similar ideas from adaptive control can be extended to safely learn the value functions of optimal control problems online using data from a single trajectory. Finally, we discuss an extension of the aforementioned approaches to richer control specifications given in the form of temporal logic formulas, which provide a formal way to express complex control objectives beyond that of stability and safety. / 2025-05-30T00:00:00Z

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The work in this thesis is on two topics. The first topic focuses on collaboration between a UAV and a UGV to track a moving ground target. The second topic focuses on deriving a guidance law for a small-scale controllable projectile to be guided into a target. For the first topic, we implement a path planning algorithm in a hardware system for a UAV and UGV to track a ground target. The algorithm is designed for urban environments where it is common for objects to obstruct sensors located on the UAV and the UGV. During the hardware system's implementation, multiple problems prevented the hardware system from functioning properly. We will describe solutions to these problems. For the second topic, we develop a guidance law for a small-scale controllable projectile using Lyapunov analysis techniques. We implement a PID controller on the body-axes pitch rate and yaw rate of the projectile such that the behavior of the pitch rate and yaw rate can be approximated as a second order system. We derive inputs for the pitch rate and yaw rate using backstepping and adaptive control techniques. The guidance law we develop guarantees the rocket will point at its intended destination. Additionally, we present expressions for the kinematics and dynamics of the rocket's motion and define the forces and moments that act on the rocket's body.

<p> The feasibility of adaptive control of a nuclear reactor is investigated. For practical reasons, an actual operating power plant is chosen, and a digital computer model developed for the reactor and associated control system. The effects of parameter variations on the transient response of the overall system are studied, and the advantages of using an adaptive controller established. An algorithm for the adaptation scheme is developed, and applied successfully to control the nuclear reactor. </p> / Thesis / Master of Engineering (MEngr)

<p> The purpose of this project was to develop an Adaptive Control Algorithm for a CNC milling machine. The milling machine is controlled by a 2100A Hewlett Packard mini-computer. The Adaptive Control Software has to operate in unison with an already available Numerical Control Software. Both these programmes are stored in the computer and the computer operates on them with the aid of the interrupt pulses received from the Time Base Generator located in the Controller.</p> <p> The Adaptive Control Software should be capable of optimising the milling process, that is enabling the milling machine to operate at the highest feed-rate without violating or overriding the maximum permissible values of the horizontal force and torque acting on the cutter. These maximum values of the force and torque are determined from the tool strength and capacities of the servo drives and spindle motor. Further, the machine should be able to arrive at the above feed-rate in the shortest possible time interval without causing cyclic variations in the feed-rate which could lead to an unstable system. The programme should be able to obtain ten samples of the parameters per revolution of the spindle. The feed-rate thus obtained (after comparing with the maximum and minimum feed-rates of the machine and making any corrections, if necessary) should be stored in a memory location accessible to the Numerical Control Programme. The instantaneous values of the force and torque are transmitted to the computer via the transducers attached on the spindle of the machine and the Analog-to-Digital Processor, therefore, the Adaptive Control Software will have to communicate with the Analog-to-Digital Processor in order to receive the values of the forces and torque. Thus the above mentioned requirements will have to be met by this piece of software. With this end in view, the following algorithm was developed.</p> <p> The algorithm consists of two portions, namely, the Data Reading Routine and the Policy Routine. The former accepts the two horizontal forces (which are phase shifted by 90°) and the torque acting on the cutter by communicating with the Analog-to-Digital Processor. However, all these three parameters are received through the same channel from the Analog-to-Digital Processor as such a method of identifying the variables was necessary. For this purpose, the Data Reading Routine consists of software capable of communicating with the Analog-to-Digital Processor at time intervals of 10 m.sec. and receiving the data in a digital form, decoding the input and ascertaining which input parameter was received. The Policy Routine has two modes of operation viz., the constraint and optimizing modes. This routine ascertains the critical error and arrives at the new feed-rate depending on the Policy used. After checking the value of this feed-rate with the maximum and minimum feed-rates available on the machine (and corrections made if necessary), the suitable value of this feed-rate is stored in a memory location accessible to the Numerical Control programme. This gives the general structure of the Adaptive Control Algorithm developed in this project.</p> / Thesis / Master of Engineering (MEngr)

The stability and safety of robotic systems are heavily impacted by delays and parametric uncertainties due to external disturbances, modeling inaccuracies, reaction forces, and variations in dynamics. This work addresses the effects of parametric uncertainties in the application of payload transportation by robotic systems that involve time delays and state constraints. The problem is split into two research questions: control of a quadrotor UAV in the presence of delays and control of robotic systems with state constraints. The first two papers explore the approaches for remotely operated quadrotors in the presence of delays and uncertainties. Specifically, the first paper surveys the existing methods for controlling a payload-carrying UAV and further presents a class of control techniques in theory that focus on time-delayed systems. The second paper proposes an adaptive control solution for the tracking control of a quadrotor UAV to transport various unknown payloads in the presence of unknown time-varying delays. The proposed controller is robust to modeling uncertainties and does not require knowledge of the uncertainties' bounds. The performance of the controller is verified on a MATLAB-SIMULINK simulated environment. The final three papers deal with enforcing state constraints on tracking control to ensure the safety of the robots in the presence of parametric uncertainties. The third paper exploits state constraints in the post-grasping scenario of the space debris disposal application. This work proposes a robust control for a space robot to follow the desired trajectory without any violation to safely grasp, carry, and release unknown payloads in their respective regions. The controller is tested in a MATLAB-SIMULINK environment with the dynamics of a planar space robot. The fourth paper introduces an adaptive control technique without any a priori knowledge of the system dynamics or the bounds of uncertainties to impose state constraints in control. The proposed controller is designed for a generic Euler-Lagrangian system in the presence of parametric uncertainties, where the state-dependent nature of the uncertainties introduces unboundedness in the overall uncertainty. The controller is validated in simulation using a robotic manipulator in a pick-and-place operation. The final paper proposes an adaptive controller for the tracking control of an experimental planar space robot. The proposed controller enforces constraints on the robot's states and their derivatives on the tracking control for transporting different payloads without any knowledge of the dynamics of the robot or the bounds of the uncertainties. The controller is validated on the experimental space robot. The stability of the proposed controllers is studied analytically using the Lyapunov theory. The results are presented with various plots and numerically analyzed on the metrics of root mean squared errors and peak errors.