Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems

Francesco Cordiano*, Marta Fochesato, Linbin Huang, Bart De Schutter*

*Corresponding author for this work

Research output: Contribution to journalConference articleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)11242-11248
Number of pages7
JournalIFAC-PapersOnLine
Volume56
Issue number2
DOIs
Publication statusPublished - 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023

Funding

Part of this research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101018826 - ERC Advanced Grant CLariNet). In addition, we wish to thank Marcello Farina and Lotfi Chaouach for the fruitful discussions.


Keywords

  • chance-constrained optimal control
  • Nonlinear model predictive control
  • stochastic systems

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