  Model predictive control (MPC) is a de facto standard control algorithm
across the process industries. There remain, however, applications where MPC is
impractical because an optimization problem is solved at each time step. We
present a link between explicit MPC formulations and manifold learning to
enable facilitated prediction of the MPC policy. Our method uses a similarity
measure informed by control policies and system state variables, to "learn" an
intrinsic parametrization of the MPC controller using a diffusion maps
algorithm, which will also discover a low-dimensional control law when it
exists as a smooth, nonlinear combination of the state variables. We use
function approximation algorithms to project points from state space to the
intrinsic space, and from the intrinsic space to policy space. The approach is
illustrated first by "learning" the intrinsic variables for MPC control of
constrained linear systems, and then by designing controllers for an unstable
nonlinear reactor.
