The aim of this dissertation is to systematically construct a hierarchical framework that allows for robust multi-agent collaborative legged locomotion. More specifically, this work provides a detailed derivation of a torque controller that is theoretically justifiable in the context of Hybrid Zero Dynamics at the lowest level of control to produce highly robust locomotion, even when subject to uncertainty. The torque controller is based on virtual constraints and partial feedback linearization and is cast into the form of a strictly convex quadratic program. This partial feedback linearization is then relaxed through the use of a defect variable, where said defect variable is allowed only to change in a manner that is consistent with rapidly exponentially stable output dynamics through the use of a Control Lyapunov Function. The torque controller is validated in both simulation and on hardware to demonstrate the efficacy of the approach. In particular, the robot is subject to payload and push disturbances and is still able to remain stable. Furthermore, the continuity of the torque controller, in addition to robustness analysis of the periodic orbit, is also provided. At the next level of control, we consider emulating the Single Rigid Body model through the use of Behavioral Systems Theory, resulting in a data-driven model that adequately describes a quadruped at the reduced-order level. Still, due to the complexity and a considerable number of variables in the problem, the model further undergoes a $2$-norm approximation, resulting in a model that is computationally efficient enough to be used in a real-time manner for trajectory planning. In order to test the method rigorously, we consider a series of experiments to examine how the planner works when using different gait parameters than that which was used during data collection. Furthermore, the planner is compared to the traditional Single Rigid Body model to test its efficacy for reference tracking. This data-driven model is then extended to the multi-agent case, where each agent is rigidly holonomically constrained to one another. In this case, the model is used in a distributed manner using a one-step communication delay such that the coupling between agents can be adequately considered while spreading the computational demand. The trajectory planner is evaluated through various hardware experiments with three agents, and simulations are also used to display the scalability of the approach by considering five robots. Finally, this dissertation examines how traditional reduced-order models can be used in tandem with data-based models to reap the benefits of both methods. More specifically, an interconnected Single Rigid Body model is considered, where the interaction forces are described via a data-driven model. Simulations are provided to display the efficacy of this approach at the reduced order level and show that the interaction forces can be reduced by considering them in the trajectory planner. As in the previous cases, this is followed by experimental evaluation subject to external forces and different terrains. / Doctor of Philosophy / The goal of this dissertation is to create a layered control scheme for teams of quadrupeds that results in stable and robust locomotion, including a high-level trajectory planner and a low-level controller. More specifically, this work outlines an optimal torque-based whole-body controller that operates at the joint level to track desired trajectories. These trajectories are obtained by a high-level trajectory planner, which utilizes a data-driven predictive controller to create an optimal trajectory without explicitly requiring knowledge of a model. The hierarchical control scheme is then extended to consider collaborative locomotion. Namely, this work considers teams of quadrupeds that are rigidly connected to one another such that there is no relative motion between them. There are potentially large interaction forces that are applied between the robots that cannot be measured, which can result in instability. Furthermore, the models used to describe the interconnected system are prohibitively complex when being used for trajectory planning. For this reason, the data-driven model considered for a single robot is extended to create a centralized model that encapsulates not only the motion of a single robot but also its connection constraints. The resulting model is very large, making it difficult to use in a real-time manner. Therefore, this work outlines how to distribute the model such that each robot can locally plan for its own motion while also considering the coupling between them. Finally, this work provides one additional extension that combines a traditional physics-based model with a data-driven model to capitalize on the strengths of each. In particular, a physics-based model is considered as a baseline, while a data-driven model is used to describe the interaction forces between robots. In using this final extension, both improved solve times and smoother locomotion are achieved. Each of the aforementioned methods is tested thoroughly through both simulations and experiments.

With the recent advances in the field of unmanned aerial vehicles, many applications have been identified. In tasks that require high-payload-to-weight ratios, flight times in the order of days, reduced noise and/or hovering capabilities, lighter-than-air vehicles present themselves as a competitive platform compared to fixed-wing and rotor based vehicles. The limiting factor in their widespread use in autonomous applications comes from the complexity of the control task. The so-called airships are highly-susceptible to aerodynamic forces and pose complex nonlinear system dynamics that complicate their modeling and control. Model-free control lends itself well as a solution to this type of problem, as it derives its control policies using input-output data, and can therefore learn complex dynamics and handle uncertain or unknown parameters and disturbances. In this work, two multi-input multi-output algorithms are presented on the basis of optimal control theory. Leveraging results from reinforcement learning, a single layer, partially connected neural network is formulated as a value function appropriator in accordance with Weierstrass higher-order approximation theorem. The so-called critic-network is updated using gradient descent methods on the mean-squared error of the temporal difference equation. In the single-network controller, the control policy is formulated as a closed form equation that is parameterized on the weights of the critic-network. A second controller is proposed that uses a second single-layer partially connected neural network, the actor-network, to calculate the control action. The actor-network is also updated using gradient descent on the squared error of the temporal difference equation. The controllers are employed in a highly realistic simulation airship model in nominal conditions and in the presence of external disturbances in the form of turbulent wind. To verify the validity and test the sensitivity of the algorithms to design parameters (the initialization of certain terms), ablation studies are carried out with multiple initial parameters. Both of the proposed algorithms are able to track the desired waypoints in both the nominal and disturbed flight tests. Furthermore, the performance of the controllers is compared to a modern, state-of-the-art multi-input multi-output controller. The two proposed controllers outperform the comparison controller in all but one flight test, with up to four fold reduction in the integral absolute error and integral time absolute error metrics. On top of the quantitative improvements seen in the proposed controllers, both controllers demonstrate a reduction in system oscillation and actuator chattering with respect to the comparison algorithm.

This dissertation examines the challenges associated with disruptions in supply chain financing and the railway transportation network. The study is divided into six chapters: In Chapter 1, we introduce the core problems under investigation. Chapter 2 investigates supply chain financing, emphasizing trade credit and bank credit—two predominant external financing mechanisms. Given the inherent uncertainties in demand, interest rates, and supplier credit ratings, this chapter introduces a stochastic programming model accounting for demand uncertainty. Subsequently, a robust optimization program is applied, whose complexity demands a specialized solution methodology. By analyzing a case study centered around a prominent U.S. retailer, the research reveals key insights into decision-making processes related to financing, the effects of bargaining power on portfolio mix and profits, and the relative importance of interest rate uncertainties over supplier credit ratings. Chapter 3 introduces a game-theoretical model designed to hedge financing risks in supply chains, with a focus on the application of insurance for both trade and bank credits. To support the design of effective supply chain finance contracts, three distinct contracts are developed, aiming to synchronize both financial and material flows within the supply chain. A significant feature of this chapter is the data-driven approach employed to address the potential bankruptcy risks that can arise from borrowing loans. Alongside this, a novel solution algorithm is introduced to solve the proposed non-convex models. A case study involving Ford Motor Company and a Chicago-based retailer enriches the research with real-world context. The findings offer several managerial insights: the strategic advantages of different insurance services vary based on the risk attitudes and profit margins of participants. For example, when a retailer operates with a lower profit margin, the use of Trade Credit Insurance (TCI) is recommended in conjunction with a risk-seeking retailer, while a risk-averse retailer might diminish the benefits of TCI. Conversely, with high profit margin retailers, the adoption of Payment Protection Insurance (PPI) is advised under all conditions. In Chapter 4, a game-theoretical model for risk mitigation within railway transportation is introduced. This model addresses random disruptions by employing strategies like repair, re-routing, third-party services, and leasing capacity from competing rail companies. Through a U.S. case study, the efficacy of these strategies is examined, with renting railcars emerging as a particularly potent approach to enhance resilience and reduce third-party expenses. The research further suggests that negotiations extending delivery dates can significantly diminish post-disruption costs. Finally, Chapter 5 summarizes the primary contributions of this research, laying the groundwork for prospective studies in this domain. / Thesis / Doctor of Philosophy (PhD)

In this thesis, we developed prognostic models of clinical outcomes, specific to violent and criminal outcomes in psychiatry, and predictive models of treatment response at an individual level. Overall, we demonstrate that evidence-based risk factors, protective factors, and treatment status variables were able to prognosticate prospective physical aggression at an individual level; 2) prognostic models of clinical and violent outcomes in psychiatry have largely focused on clinical and sociodemographic variables, show similar performance between identifying true positives and true negatives, although the error rate of models are still high, and further refinement is needed; 3) within treatment response prediction models in MDD using EEG, greater performance was observed in predicting response to rTMS, relative to antidepressants, and across models, greater sensitivity (true positives), were observed relative to specificity (true negatives), suggesting that EEG prediction models thus far better identify non-responders than responders; and 4) across randomized clinical trials using data-driven biomarkers in predictive models, based on the consistency of performance across models with large sample sizes, the highest degree of evidence was in predicting response to sertraline and citalopram using fMRI features. / Dissertation / Doctor of Philosophy (PhD)

Asynchronous design is a possible alternative design methodology that has the ability to alleviate issues associated with clock skew, power dissipation, and process and environmental variability among transistors, issues encountered in typical synchronous design methodologies. This investigation studies the implementation of two asynchronous models of the Texas Instruments MSP430 processor family using a logic system known as Null Convention Logic (NCL). The study also investigates two design styles of NCL: the data-driven and control-driven design styles. This example and others show that although there are tradeoffs in chip area and performance, the control-driven design style is a viable methodology that can lead to designs that are low in energy usage. The openMSP430 processor project is the baseline for the investigation as it is a mature open-source project. Silicon-proven multiple times and fully synthesizable, it parallels the original Texas Instruments family nearly cycle for cycle. UNCLE (Unified NCL Environment) is a toolset used to create comparable implementations of the openMSP430 architecture that are data-driven and control-driven in nature. This investigation shows that the control-driven implementation has a slightly larger chip area due to the complexity of the control path and its effects on the data path. While the control path has a lower area than the data-driven model due to area optimization, the data path of the control-driven version is larger than that of the data-driven model. Because of these issues of complexity in both the control and data paths, the performance of the model suffers as well, degrading from the already poor performance of the traditional data-driven NCL model. Along with the increase in chip area and the decrease in performance, the control-driven model sees a 50.2% average decrease in energy usage as compared to the data-driven model. As with most design choices in engineering, there are tradeoffs when using either design style of NCL. This investigation serves to allow designers to make a well-informed decision when deciding between the two.

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