Differentially Flat Learning-based Model Predictive Control Using a
  Stability, State, and Input Constraining Safety Filter
Adam W. Hall Melissa Greeff Angela P. Schoellig
Learning-based optimal control algorithms control unknown systems using past
trajectory data and a learned model of the system dynamics. These controllers
use either a linear approximation of the learned dynamics, trading performance
for faster computation, or nonlinear optimization methods, which typically
perform better but can limit real-time applicability. In this work, we present
a novel nonlinear controller that exploits differential flatness to achieve
similar performance to state-of-the-art learning-based controllers but with
significantly less computational effort. Differential flatness is a property of
dynamical systems whereby nonlinear systems can be exactly linearized through a
nonlinear input mapping. Here, the nonlinear transformation is learned as a
Gaussian process and is used in a safety filter that guarantees, with high
probability, stability as well as input and flat state constraint satisfaction.
This safety filter is then used to refine inputs from a flat model predictive
controller to perform constrained nonlinear learning-based optimal control
through two successive convex optimizations. We compare our method to
state-of-the-art learning-based control strategies and achieve similar
performance, but with significantly better computational efficiency, while also
respecting flat state and input constraints, and guaranteeing stability.