Optimal stochastic tracking control for brain network dynamics

Network control theory (NCT) has recently been utilized in neuroscience to facilitate our understanding of brain stimulation effects and explore optimal paradigms. This paper considers stochastic brain dynamics and introduces optimal stochastic tracking control to synchronize brain dynamics to target dynamics rather than to a target state at a specific time point. For all participants, we utilize a gradient descent optimization method to estimate the parameters (e.g., the coupled matrix and the variance matrix) for the brain network dynamical system. We then utilize optimal stochastic tracking control techniques to drive the original unhealthy dynamics by controlling a certain number of nodes to synchronize with target healthy dynamics. Results show that the tracking energy is negatively correlated with the average controllability of the brain network system, while the energy of the optimal state transfer control is significantly related to the target state value. For a 100-dimensional system, the dynamics over 90% of the nodes can be improved by controlling five nodes with the lowest tracking energy. These findings highlight the potential of stochastic tracking control as a promising approach for guiding brain stimulation interventions in the treatment of neurological disorders such as stroke.