Deep brain stimulation is a therapeutic treatment for a variety of neurological disorders such as Parkinson’s disease, which is hypothesized to be due to pathological synchronization of neural activity in the motor control region of the brain.  This motivates the control objective of desynchronizing neural activity using a single electrical stimulus.  Challenges include high-dimensionality, nonlinear effects, underactuation, and constraints on allowable control inputs. Various approaches have been developed to overcome these challenges, including chaotic desynchronization in which the control is chosen to maximize the Lyapunov exponent associated with phase differences for the neurons, optimal phase resetting in which an input drives the system to the phaseless set where the neurons are particularly sensitive to noise, and phase density control in which an input drives the system toward a desired phase distribution [1]. This presentation will discuss these approaches, plus recent work which shows that phase resetting can be improved by using the stochastic Hamilton-Jacobi-Bellman equation to calculate optimal inputs.

[1] D. Wilson and J. Moehlis, Recent advances in the analysis and control of large populations of neural oscillators, Annual Reviews in Control, 54: 327-351, 2022.