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Optimal Control Of Weakly Forced Nonlinear Oscillators, Isuru Sammana Dasanayake

All Theses and Dissertations (ETDs)

Optimal control of nonlinear oscillatory systems poses numerous theoretical and computational challenges. Motivated by applications in neuroscience, we develop tools and methods to synthesize optimal controls for nonlinear oscillators described by reduced order dynamical systems. Control of neural oscillations by external stimuli has a broad range of applications, ranging from oscillatory neurocomputers to deep brain stimulation for Parkinson's disease. In this dissertation, we investigate fundamental limits on how neuron spiking behavior can be altered by the use of an external stimulus: control). Pontryagin's maximum principle is employed to derive optimal controls that lead to desired spiking times of a neuron …