  How does our nervous system successfully acquire feedback control strategies
in spite of a wide spectrum of response dynamics from different
musculo-skeletal systems? The cerebellum is a crucial brain structure in
enabling precise motor control in animals. Recent advances suggest that
synaptic plasticity of cerebellar Purkinje cells involves molecular mechanisms
that mimic the dynamics of the efferent motor system that they control allowing
them to match the timing of their learning rule to behavior. Counter-Factual
Predictive Control (CFPC) is a cerebellum-based feed-forward control scheme
that exploits that principle for acquiring anticipatory actions. CFPC extends
the classical Widrow-Hoff/Least Mean Squares by inserting a forward model of
the downstream closed-loop system in its learning rule. Here we apply that same
insight to 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
rather than being exclusively confined to cerebellar learning, the approach of
controlling plasticity with a forward model of the subsystem controlled, an
approach that we term as Model-Enhanced Least Mean Squares (ME-LMS), can
provide a solution to wide set of adaptive control problems.
