We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic outcomes by tailoring the parameters of a DBS system, typically via electrical stimulation, in real time based on the patient's ongoing neuronal activity. We approximate the value function offline using a neural network to enable generating controls (stimuli) in real time via the feedback form. The neuronal activity is characterized by a nonlinear, stiff system of differential equations as dictated by the Hodgkin-Huxley model. Our training process leverages the relationship between Pontryagin's maximum principle and Hamilton-Jacobi-Bellman equations to update the value function estimates simultaneously. Our numerical experiments illustrate the accuracy of our approach for out-of-distribution samples and the robustness to moderate shocks and disturbances in the system.

The work presented in this report introduces a framework aimed towards learning to imitate human gaits. Humans exhibit movements like walking, running, and jumping in the most efficient manner, which served as the source of motivation for this project. Skeletal and Musculoskeletal human models were considered for motions in the sagittal plane, and results from both were compared exhaustively. While skeletal models are driven with motor actuation, musculoskeletal models perform through muscle-tendon actuation. Model-free reinforcement learning algorithms were used to optimize inverse dynamics control actions to satisfy the objective of imitating a reference motion along with secondary objectives of minimizing effort in terms of power spent by motors and metabolic energy consumed by the muscles. On the one hand, the control actions for the motor actuated model is the target joint angles converted into joint torques through a Proportional-Differential controller. While on the other hand, the control actions for the muscle-tendon actuated model is the muscle excitations converted implicitly to muscle activations and then to muscle forces which apply moments on joints. Muscle-tendon actuated models were found to have superiority over motor actuation as they are inherently smooth due to muscle activation dynamics and don't need any external regularizers. Finally, a strategy that was used to obtain an optimal configuration of the significant decision variables in the framework was discussed. All the results and analysis are presented in an illustrative, qualitative, and quantitative manner. Supporting video links are provided in the Appendix.