  Nonlinear receding horizon model predictive control is a powerful approach to
controlling nonlinear dynamical systems. However, typical approaches that use
the Jacobian, adjoint, and forward-backward passes may lose fidelity and
efficacy for highly nonlinear problems. Here, we develop an Ensemble Model
Predictive Control (EMPC) approach wherein the forward model remains fully
nonlinear, and an ensemble-represented Gaussian process performs the backward
calculations to determine optimal gains for the initial time. EMPC admits black
box, possible non-differentiable models, simulations are executable in parallel
over long horizons, and control is uncertainty quantifying and applicable to
stochastic settings. We construct the EMPC for terminal control and regulation
problems and apply it to the control of a quadrotor in a simulated,
identical-twin study. Results suggest that the easily implemented approach is
promising and amenable to controlling autonomous robotic systems with added
state/parameter estimation and parallel computing.
