Adaptive Strategies for Oscillatory Systems:Integrating Machine Learning and ControlTechniques with Applications in Neuroscience

Oscillators are ubiquitous in nature. As such, a significant body of literature has been devoted to studying their dynamics and how to control those dynamics. Many systems, however, do not maintain the core assumptions guiding the development of this literature-- systems that are either too complex or too poorly understood to allow for simple mathematical representations. Machine learning can serve as a powerful tool to supplement our understanding of dynamical systems in situations where traditional methods fail. In this dissertation, we develop first a control strategy for oscillators using standard techniques and assumptions about our dynamical system, then explore the ways in which machine learning can replace some of the strictest requirements on developing control strategies. We demonstrate how machine learning can extract meaningful information from complex systems in neuroscience and use that information as the basis for control. Lastly, we discuss some emerging strategies for further marrying the disciplines of dynamics and control and machine learning