Tuning Functions Based Adaptive Synchrony in Inferior Olive Neurons

The design of an adaptive control system for the synchronization of inferior olive neurons (IONs) is the subject of this paper. Clusters of inferior olive neurons in the olive-cerebellar system play an important role in providing synchronized motor control signals for the activation of large number of muscles. The orbits of IONs evolving from arbitrary initial conditions are not synchronized. The objective is to design a control law such that the controlled ION tracks the trajectories of the reference ION. The derivation of the control law is based on the tuning functions method and is completed in two steps of a backstopping design process. Using Lyapunov analysis, it is shown that in the closed-loop system, the controlled ION asymptotically tracks the trajectories of the reference ION. Simulation results are presented which show precise synchronization of the two IONs.