  This paper proposes an off-line algorithm, called Recurrent Model Predictive
Control (RMPC), to solve general nonlinear finite-horizon optimal control
problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can
make full use of the current computing resources and adaptively select the
longest model prediction horizon. Our algorithm employs a recurrent function to
approximate the optimal policy, which maps the system states and reference
values directly to the control inputs. The number of prediction steps is equal
to the number of recurrent cycles of the learned policy function. With an
arbitrary initial policy function, the proposed RMPC algorithm can converge to
the optimal policy by directly minimizing the designed loss function. We
further prove the convergence and optimality of the RMPC algorithm thorough
Bellman optimality principle, and demonstrate its generality and efficiency
using two numerical examples.
