Koopman Approximator based Adaptive Model Predictive Control of
Continuous Nonlinear Systems
Abstract
This paper considers the real-time control of a class of complex
continuous nonlinear systems with an increasing requirement on control
accuracy and unknown dynamics at the start time due to their complex
dynamics and uncertainties. A Koopman approximate model-based adaptive
MPC design using the Lyapunov technique is explored. Specifically, the
nonlinear system is modeled/transformed into a linear model in a lifting
space with the Koopman operator. A recursive update of the approximator
is provided by which the parameters set of the approximator is in a
nested form and a shrinking of the boundary of the approximator’s
mismatch from the real system is obtained. Also, based on the Koopman
model and its mismatch boundary, a sufficient condition that ensures the
states of the nonlinear system eventually converge to a small
neighborhood of the origin is deduced. An FCCU example is employed to
show the effectiveness of the proposed control law.