  Nonlinear optimal control problems are often solved with numerical methods
that require knowledge of system's dynamics which may be difficult to infer,
and that carry a large computational cost associated with iterative
calculations. We present a novel neurobiologically inspired hierarchical
learning framework, Reinforcement Learning Optimal Control, which operates on
two levels of abstraction and utilises a reduced number of controllers to solve
nonlinear systems with unknown dynamics in continuous state and action spaces.
Our approach is inspired by research at two levels of abstraction: first, at
the level of limb coordination human behaviour is explained by linear optimal
feedback control theory. Second, in cognitive tasks involving learning symbolic
level action selection, humans learn such problems using model-free and
model-based reinforcement learning algorithms. We propose that combining these
two levels of abstraction leads to a fast global solution of nonlinear control
problems using reduced number of controllers. Our framework learns the local
task dynamics from naive experience and forms locally optimal infinite horizon
Linear Quadratic Regulators which produce continuous low-level control. A
top-level reinforcement learner uses the controllers as actions and learns how
to best combine them in state space while maximising a long-term reward. A
single optimal control objective function drives high-level symbolic learning
by providing training signals on desirability of each selected controller. We
show that a small number of locally optimal linear controllers are able to
solve global nonlinear control problems with unknown dynamics when combined
with a reinforcement learner in this hierarchical framework. Our algorithm
competes in terms of computational cost and solution quality with sophisticated
control algorithms and we illustrate this with solutions to benchmark problems.
