Learning-Based Nonlinear Model Predictive Control with Accurate Uncertainty Compensation

A learning-based nonlinear model predictive
control (LBNMPC) method is proposed in this
paper for general nonlinear systems under system
uncertainties and subject to state and input constraints.
The proposed LBNMPC strategy decouples the
robustness and performance requirements by employing
an additional learned model and introducing it into
the MPC framework along with the nominal model.
The nominal model helps to ensure the closed-loop
system’s safety and stability, and the learned model
aims to improve the tracking behaviors. As a core of
the learned model construction, an online parameter
estimator is designed to deal with system uncertainties.
This estimation process effectively evaluates both
the current and historical effects of uncertainties,
leading to superior estimating performance compared
with conventional methods. By constructing an invariant
terminal constraint set, we prove that the
LBNMPC is recursively feasible and robustly asymptotically
stable. Numerical verifications for a two-link
manipulator are conducted to validate the effectiveness
and robustness of the proposed control scheme.