Cerebellar-inspired learning rule for gain adaptation of feedback controllers

The cerebellum is a crucial brain structure in enabling precise motor control in animals. Recent advances suggest that the timing of the plasticity rule of Purkinje cells, the main cells of the cerebellum, is matched to behavioral function. Simultaneously, counter-factual predictive control (CFPC), a cerebellar-based control scheme, has shown that the optimal rule for learning feed-forward action in an adaptive filter playing the role of the cerebellum must include a forward model of the system controlled. Here we show how the same learning rule obtained in CFPC, which we term as Model-enhanced least mean squares (ME-LMS), emerges in the problem of learning the gains of a feedback controller. To that end, we frame a model-reference adaptive control (MRAC) problem and derive an adaptive control scheme treating the gains of a feedback controller as if they were the weights of an adaptive linear unit. Our results demonstrate that the approach of controlling plasticity with a forward model of the subsystem controlled can provide a solution to a wide set of adaptive control problems.