In this dissertation, new data-driven techniques are developed to solve three problems related to generating predictive models of the immune system. These problems and their solutions are summarized as follows. The first problem is that, while cellular characteristics can be measured using flow cytometry, immune system cells are often analyzed only after they are sorted into groups by those characteristics. In Chapter 3 a method of analyzing the cellular characteristics of the immune system cells by generating Probability Density Functions (PDFs) to model the flow cytometry data is proposed. To generate a PDF to model the distribution of immune cell characteristics a new class of random variable called Sliced-Distributions (SDs) is developed. It is shown that the SDs can outperform other state-of-the-art methods on a set of benchmarks and can be used to differentiate between immune cells taken from healthy patients and those with Rheumatoid Arthritis. The second problem is that while immune system cells can be broken into different subpopulations, it is unclear which subpopulations are most significant. In Chapter 4 a new machine learning algorithm is formulated and used to identify subpopulations that can best predict disease severity or the populations of other immune cells. The proposed machine learning algorithm performs well when compared to other state-of-the-art methods and is applied to an immunological dataset to identify disease-relevant subpopulations of immune cells denoted immune states. Finally, while immunotherapies have been effectively used to treat cancer, selecting an optimal drug dose and period of treatment administration is still an open problem. In Chapter 5 a method to estimate Lyapunov functions of a system with unknown dynamics is proposed. This method is applied to generate a semialgebraic set containing immunotherapy doses and period of treatment that is predicted to eliminate a patient's tumor. The problem of selecting an optimal pulsed immunotherapy treatment from this semialgebraic set is formulated as a Global Polynomial Optimization (GPO) problem. In Chapter 6 a new method to solve GPO problems is proposed and optimal pulsed immunotherapy treatments are identified for this system.

JOOEE is a cube-shaped lunar robot with a simple yet robust design. JOOEE ishermetically sealed from its environment with no external actuators. Instead, JOOEE spins three internal orthogonal flywheels to accumulate angular momentum and uses a solenoid brake at each wheel to transfer the angular momentum to the body. This procedure allows JOOEE to jump and hop along the lunar surface. The sudden transfer in angular momentum during braking causes discontinuities in JOOEE’s dynamics that are best described using a hybrid control framework. Due to the irregular methods of locomotion, the limited resources on the lunar surface, and the unique mission objectives, optimal control profiles are desired to minimize performance metrics such as time, energy, and impact velocity during different maneuvers. This paper details the development of an optimization tool that can handle JOOEE’s dynamics including the design of a hybrid control framework, dynamics modeling and discretization, optimization cost functions and constraints, model validation, and code acceleration techniques.