The aim of this thesis is to study adaptive controllers in the context of a Pro-portional Integral Derivative (PID) controller. The PID controller is tuned via loop shaping techniques to ensure desired robustness and performance characteristics with respect to a target loop shape. There are two problems that this work addresses: Consider a system that is controlled via an adaptive PID controller. If in absence of or under lack of excitation, the system or controller parameters drift to an arbitrary system (that may or may not be stable). Then, once the system gets sufficient ex- citation, there are two questions to be addressed: First, how quickly is the system able to recover to the target system, and in the process of recovery, how large are the transient overshoots and what factors affect the recovery of the drifted system? Second, continuous online adaptation of the controller may not always be necessary (and economical). So, is there a means to monitor the performance of the current controller and determine via robustness conditions whether to continue with the same controller or reject it and adapt to a new controller? Hence, this work is concerned with robust performance monitoring and recovery of an adaptive PID control system that had drifted to another system in absence of sufficient excitation or excessive noise.

The objective of this thesis is to propose two novel interval observer designs for different classes of linear and hybrid systems with nonlinear observations. The first part of the thesis presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations. The observer is constructed using mixed-monotone decompositions, which ensures correctness and positivity without additional constraints/assumptions. The proposed design also involves additional degrees of freedom that may improve the performance of the observer design. The proposed observer is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. The observer gains are computed using mixed-integer (linear) programs. The second part of the thesis addresses the problem of designing a novel asymptotically stable interval estimator design for hybrid systems with nonlinear dynamics and observations under the assumption of known jump times. The proposed architecture leverages mixed-monotone decompositions to construct a hybrid interval observer that is guaranteed to frame the true states. Moreover, using common Lyapunov analysis and the positive/cooperative property of the error dynamics, two approaches were proposed for constructing the observer gains to achieve uniform asymptotic stability of the error system based on mixed-integer semidefinite and linear programs, and additional degrees of freedom are incorporated to provide potential advantages similar to coordinate transformations. The effectiveness of both observer designs is demonstrated through simulation examples.

Unmanned aerial vehicles (UAVs) have revolutionized various fields, but their use in dynamic environments is still limited due to safety concerns arising from sensor malfunctions and localization errors. Inspired by birds, which exhibit unparalleled maneuverability and adaptability to dynamic environments by synergizing mechanical compliance with control, this research focused on developing a new generation of bio-inspired soft/compliant UAVs with mechanical intelligence that can withstand collisions and enable aerial interaction. The proposed approach is to harness collision energies and switch into the next favorable configuration, which helps retain stability and successfully fly even in the presence of external forces. It investigated various types of active/passive reconfigurable UAVs to demonstrate this idea. The first approach looked into designs of compliant reconfigurable quadrotors by employing springs which can reduce their dimension under external forces, thereby sustaining 2D planar collision forces and enabling flights through narrow gaps in a squeeze-and-fly manner. Next, fabric-based soft UAVs made of pneumatic beams were successfully explored to design lightweight and collision-resilient quadrotors to demonstrate 3D collision-resilience and impact-based perching. This research contributes to thorough modeling of the unique dynamics of these reconfigurable quadrotors and proposes various adaptive and learning-based controllers for robust low-level tracking. Finally, these controllers were integrated into a novel collision-inclusive motion planning framework based-on optimal control theory to perform physical interaction tasks, such as contact-based navigation, mapping, and inspection. In essence, this research redefines safety for UAVs and expands their capabilities for contact-rich tasks.

Multi-segment manipulators and mobile robot collectives are examples of multi-agent robotic systems, in which each segment or robot can be considered an agent. Fundamental motion control problems for such systems include the stabilization of one or more agents to target configurations or trajectories while preventing inter-agent collisions, agent collisions with obstacles, and deadlocks. Despite extensive research on these control problems, there are still challenges in designing controllers that (1) are scalable with the number of agents; (2) have theoretical guarantees on collision-free agent navigation; and (3) can be used when the states of the agents and the environment are only partially observable. Existing centralized and distributed control architectures have limited scalability due to their computational complexity and communication requirements, while decentralized control architectures are often effective only under impractical assumptions that do not hold in real-world implementations. The main objective of this dissertation is to develop and evaluate decentralized approaches for multi-agent motion control that enable agents to use their onboard sensors and computational resources to decide how to move through their environment, with limited or absent inter-agent communication and external supervision. Specifically, control approaches are designed for multi-segment manipulators and mobile robot collectives to achieve position and pose (position and orientation) stabilization, trajectory tracking, and collision and deadlock avoidance. These control approaches are validated in both simulations and physical experiments to show that they can be implemented in real-time while remaining computationally tractable. First, kinematic controllers are proposed for position stabilization and trajectory tracking control of two- or three-dimensional hyper-redundant multi-segment manipulators. Next, robust and gradient-based feedback controllers are presented for individual holonomic and nonholonomic mobile robots that achieve position stabilization, trajectory tracking control, and obstacle avoidance. Then, nonlinear Model Predictive Control methods are developed for collision-free, deadlock-free pose stabilization and trajectory tracking control of multiple nonholonomic mobile robots in known and unknown environments with obstacles, both static and dynamic. Finally, a feedforward proportional-derivative controller is defined for collision-free velocity tracking of a moving ground target by multiple unmanned aerial vehicles.

Soft continuum robots with the ability to bend, twist, elongate, and shorten, similar to octopus arms, have many potential applications, such as dexterous manipulation and navigation through unstructured, dynamic environments. Novel soft materials such as smart hydrogels, which change volume and other properties in response to stimuli such as temperature, pH, and chemicals, can potentially be used to construct soft robots that achieve self-regulated adaptive reconfiguration through on-demand dynamic control of local properties. However, the design of controllers for soft continuum robots is challenging due to their high-dimensional configuration space and the complexity of modeling soft actuator dynamics. To address these challenges, this dissertation presents two different model-based control approaches for robots with distributed soft actuators and sensors and validates the approaches in simulations and physical experiments. It is demonstrated that by choosing an appropriate dynamical model and designing a decentralized controller based on this model, such robots can be controlled to achieve diverse types of complex configurations. The first approach consists of approximating the dynamics of the system, including its actuators, as a linear state-space model in order to apply optimal robust control techniques such as H∞ state-feedback and H∞ output-feedback methods. These techniques are designed to utilize the decentralized control structure of the robot and its distributed sensing and actuation to achieve vibration control and trajectory tracking. The approach is validated in simulation on an Euler-Bernoulli dynamic model of a hydrogel based cantilevered robotic arm and in experiments with a hydrogel-actuated miniature 2-DOF manipulator. The second approach is developed for soft continuum robots with dynamics that can be modeled using Cosserat rod theory. An inverse dynamics control approach is implemented on the Cosserat model of the robot for tracking configurations that include bending, torsion, shear, and extension deformations. The decentralized controller structure facilitates its implementation on robot arms composed of independently-controllable segments that have local sensing and actuation. This approach is validated on simulated 3D robot arms and on an actual silicone robot arm with distributed pneumatic actuation, for which the inverse dynamics problem is solved in simulation and the computed control outputs are applied to the robot in real-time.

Localization tasks using two-way ranging (TWR) are making headway in modern daynavigation applications as an alternative to legacy global navigation satellite systems (GNSS) such as GPS. There is not currently literature that provides a closed-form expression for estimation performance bounds on position and attitude when a TWR system is employed. A Cramer-Rao Lower Bounds (CRLB) is derived for position and orientation estimation using both 2-D and 3-D geometries. A literature review is performed to give background and detail on the tools needed for a thorough analysis of this problem. Popular Least Squares techniques and solutions to Wahba’s problem are compared to the derived bounds as proof of correctness using Monte Carlo simulations. A brief exploration on estimation performance using an Extended Kalman Filter for non-stationary users is also looked at as an introduction to future extensions to this work. The literature Applications like the CHP2 system are discussed as well to show how secure, inexpensive and robust implementation of TWR is highly feasible. i

Due to their effectiveness in capturing similarities between different entities, graphical models are widely used to represent datasets that reside on irregular and complex manifolds. Graph signal processing offers support to handle such complex datasets. By extending the digital signal processing conceptual frame from time and frequency domain to graph domain, operators such as graph shift, graph filter and graph Fourier transform are defined. In this dissertation, two novel graph filter design methods are proposed. First, a graph filter with multiple shift matrices is applied to semi-supervised classification, which can handle features with uneven qualities through an embedded feature importance evaluation process. Three optimization solutions are provided: an alternating minimization method that is simple to implement, a convex relaxation method that provides a theoretical performance benchmark and a genetic algorithm, which is computationally efficient and better at configuring overfitting. Second, a graph filter with splitting-and-merging scheme is proposed, which splits the graph into multiple subgraphs. The corresponding subgraph filters are trained parallelly and in the last, by merging all the subgraph filters, the final graph filter is obtained. Due to the splitting process, the redundant edges in the original graph are dropped, which can save computational cost in semi-supervised classification. At the same time, this scheme also enables the filter to represent unevenly sampled data in manifold learning. To evaluate the performance of the proposed graph filter design approaches, simulation experiments with synthetic and real datasets are conduct. The Monte Carlo cross validation method is employed to demonstrate the need for the proposed graph filter design approaches in various application scenarios. Criterions, such as accuracy, Gini score, F1-score and learning curves, are provided to analyze the performance of the proposed methods and their competitors.

Operational efficiency of solar energy farms requires detailed analytics and information on each panel regarding voltage, current, temperature, and irradiance. Monitoring utility-scale solar arrays was shown to minimize the cost of maintenance and help optimize the performance of photovoltaic (PV) arrays under various conditions. This dissertation describes a project that focuses on the development of machine learning and neural network algorithms. It also describes an 18kW solar array testbed for the purpose of PV monitoring and control. The use of the 18kW Sensor Signal and Information Processing (SenSIP) PV testbed which consists of 104 modules fitted with smart monitoring devices (SMDs) is described in detail. Each of the SMDs has embedded, a wireless transceiver, and relays that enable continuous monitoring, fault detection, and real-time connection topology changes. Data is obtained in real time using the SenSIP PV testbed. Machine learning and neural network algorithms for PV fault classification is are studied in depth. More specifically, the development of a series of customized neural networks for detection and classification of solar array faults that include soiling, shading, degradation, short circuits and standard test conditions is considered. The evaluation of fault detection and classification methods using metrics such as accuracy, confusion matrices, and the Risk Priority Number (RPN) is performed. The examination and assessment the classification performance of customized neural networks with dropout regularizers is presented in detail. The development and evaluation of neural network pruning strategies and illustration of the trade-off between fault classification model accuracy and algorithm complexity is studied. This study includes data from the National Renewable Energy Laboratory (NREL) database and also real-time data collected from the SenSIP testbed at MTW under various loading and shading conditions. The overall approach for detection and classification promises to elevate the performance and robustness of PV arrays.

This dissertation presents a comprehensive study of modeling and control issues associated with nonholonomic differential drive mobile robots. The first part of dissertation focuses on modeling using Lagrangian mechanics. The dynamics is modeled as a two-input two-output (TITO) nonlinear model. Motor dynamics are also modeled. Trade studies are conducted to shed light on critical vehicle design parameters, and how they impact static properties, dynamic properties, directional stability, coupling and overall vehicle design. An aspect ratio based dynamic decoupling condition is also presented. The second part of dissertation addresses design of linear time-invariant (LTI), multi-input multi-ouput (MIMO) fixed-structure H∞ controllers for the inner-loop velocity (v, ω) tracking system of the robot, motivated by a practical desire to design classically structured robust controllers. The fixed-structure H∞-optimal controllers are designed using Generalized Mixed Sensitivity(GMS) methodology to systematically shape properties at distinct loop breaking points. The H∞-control problem is solved using nonsmooth optimization techniques to compute locally optimal solutions. Matlab’s Robust Control toolbox (Hinfstruct and Systune) is used to solve the nonsmooth optimization. The dissertation also addresses the design of fixed-structure MIMO gain-scheduled H∞ controllers via GMS methodology. Trade-off studies are conducted to address the effect of vehicle design parameters on frequency and time domain properties of the inner-loop control system of mobile robot. The third part of dissertation focuses on the design of outer-loop position (x, y, θ) control system of mobile robot using real-time model predictive control (MPC) algorithms. Both linear time-varying (LTV) MPC and nonlinear MPC algorithms are discussed.The outer-loop performance of mobile robot is studied for two applications - 1) single robot trajectory tracking and multi-robot coordination in presence of obstacles, 2) maximum progress maneuvering on racetrack. The dissertation specifically addresses the impact of variation of c.g. position w.r.t. wheel-axle on directional maneuverability, peak control effort required to perform aggressive maneuvers, and overall position control performance. Detailed control relevant performance trade-offs associated with outer-loop position control are demonstrated through simulations in discrete time. Optimizations packages CPLEX(convex-QP in LTV-MPC) and ACADO(NLP in nonlinear-MPC) are used to solve the OCP in real time. All simulations are performed on Robot Operating System (ROS).

This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck) regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current (DC-AC) inverter. These are widely used for power transfer in a variety of industrial and personal applications. This motivates the precise quantification of conditions under which existing modeling and design methods yield satisfactory designs, and the study of alternatives when they don’t. This dissertation describes a method utilizing Fourier components of the input square wave and the inductor-capacitor (LC) filter transfer function, which doesn’t require the small ripple approximation. Then, trade-offs associated with the choice of the filter order are analyzed for integrated buck converters with a constraint on their chip area. Design specifications which would justify using a fourth or sixth order filter instead of the widely used second order one are examined. Next, sampled-data (SD) control of a buck converter is analyzed. Three methods for the digital controller design are studied: analog design followed by discretization, direct digital design of a discretized plant, and a “lifting” based method wherein the sampling time is incorporated in the design process by lifting the continuous-time design plant before doing the controller design. Specifically, controller performance is quantified by studying the induced-L2 norm of the closed loop system for a range of switching/sampling frequencies. In the final segment of this dissertation, the inner-outer control loop, employed in inverters with an inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the loop broken at the error and the control are examined, demonstrating that traditional methods only address these properties for one loop-breaking point. New controllers are then provided for improving both sets of properties.