Reference:
F. Cordiano,
M. Fochesato,
L. Huang, and
B. De Schutter,
"Provably-stable stochastic MPC for a class of nonlinear contractive
systems," Proceedings of the 22nd IFAC World Congress,
Yokohama, Japan, pp. 11242-11248, July 2023.
Abstract:
We present a model predictive control framework for a class of
nonlinear systems affected by additive stochastic disturbances with
(possibly) unbounded support. We consider hard input constraints and
chance state constraints and we employ the unscented transform method
to propagate the disturbances over the nonlinear dynamics in a
computationally efficient manner. The main contribution of our work is
the establishment of sufficient conditions for stability and recursive
feasibility of the closed-loop system, based on the design of a
terminal cost and a terminal set. We focus here on a special class of
nonlinear systems that exhibit contractive properties in the dynamics.
By assuming this property, we propose a novel approach to efficiently
compute the terminal conditions without the need of performing any
linearization of the dynamics. Finally, we provide an illustrative
example to corroborate our theoretical findings.