A Multirate Variational Approach to Nonlinear MPC

A nonlinear model predictive control (NMPC) approach is proposed based on a variational representation of the system model and the receding horizon optimal control problem. The proposed tube-based convex MPC approach provides improvements in model accuracy and computational efficiency, and allows for alternative means of computing linearization error bounds. To this end we investigate the use of single rate and multirate system representations derived from a discrete variational principle to obtain structure-preserving time-stepping schemes. We show empirically that the desirable conservation properties of the discrete time model are inherited by the optimal control problem. Model linearization is achieved either by direct Jacobian Linearization or by quadratic and linear Taylor series approximations of the Lagrangian and generalized forces respectively. These two linearization schemes are proved to be equivalent for a specific choice of approximation points. Using the multirate variational formulation we derive a novel multirate NMPC approach, and show that it can provide large computational savings for systems with dynamics or control inputs evolving on different time scales.