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

Francesco Cordiano; Marta Fochesato; Linbin Huang; Bart De Schutter

doi:10.1016/j.ifacol.2023.10.313

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 journal › Conference article › Scientific › peer-review

2 Citations (Scopus)

71 Downloads (Pure)

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 language	English
Pages (from-to)	11242-11248
Number of pages	7
Journal	IFAC-PapersOnLine
Volume	56
Issue number	2
DOIs	https://doi.org/10.1016/j.ifacol.2023.10.313
Publication status	Published - 2023
Event	22nd IFAC World Congress - Yokohama, Japan Duration: 9 Jul 2023 → 14 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

Access to Document

10.1016/j.ifacol.2023.10.313

1-s2.0-S2405896323006808-mainFinal published version, 520 KBLicence: CC BY-NC-ND

Cite this

@article{f0c77659b0284dc781036c59e38dac2f,

title = "Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems",

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.",

keywords = "chance-constrained optimal control, Nonlinear model predictive control, stochastic systems",

author = "Francesco Cordiano and Marta Fochesato and Linbin Huang and \{De Schutter\}, Bart",

year = "2023",

doi = "10.1016/j.ifacol.2023.10.313",

language = "English",

volume = "56",

pages = "11242--11248",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "2",

note = "22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",

}

TY - JOUR

T1 - Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems

AU - Cordiano, Francesco

AU - Fochesato, Marta

AU - Huang, Linbin

AU - De Schutter, Bart

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - chance-constrained optimal control

KW - Nonlinear model predictive control

KW - stochastic systems

UR - https://www.scopus.com/pages/publications/85183660832

U2 - 10.1016/j.ifacol.2023.10.313

DO - 10.1016/j.ifacol.2023.10.313

M3 - Conference article

AN - SCOPUS:85183660832

SN - 2405-8963

VL - 56

SP - 11242

EP - 11248

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 2

T2 - 22nd IFAC World Congress

Y2 - 9 July 2023 through 14 July 2023

ER -

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

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this