A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints

Matteo Rubagotti, Gian Paolo Incremona, Antonella Ferrara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5940-5945
Number of pages6
ISBN (Electronic)9781538613955
DOIs
Publication statusPublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Input Constraints
State Constraints
Sliding mode control
Sliding Mode Control
Linear systems
Discrete-time
Linear Systems
Optimization
Disturbance
Constraint Satisfaction
Convergence Time
Finite Horizon
Model predictive control
Model Predictive Control
Merging
Instant
Control Strategy
Optimal Control Problem
Boundary Layer
Boundary layers

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Rubagotti, M., Paolo Incremona, G., & Ferrara, A. (2019). A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 5940-5945). [8619503] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619503

A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints. / Rubagotti, Matteo; Paolo Incremona, Gian; Ferrara, Antonella.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 5940-5945 8619503 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rubagotti, M, Paolo Incremona, G & Ferrara, A 2019, A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619503, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 5940-5945, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619503
Rubagotti M, Paolo Incremona G, Ferrara A. A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 5940-5945. 8619503. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619503
Rubagotti, Matteo ; Paolo Incremona, Gian ; Ferrara, Antonella. / A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 5940-5945 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{5a85833354c947d0b50780e0972318a8,
title = "A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints",
abstract = "This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.",
author = "Matteo Rubagotti and {Paolo Incremona}, Gian and Antonella Ferrara",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619503",
language = "English",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "5940--5945",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",
address = "United States",

}

TY - GEN

T1 - A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints

AU - Rubagotti, Matteo

AU - Paolo Incremona, Gian

AU - Ferrara, Antonella

PY - 2019/1/18

Y1 - 2019/1/18

N2 - This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.

AB - This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.

UR - http://www.scopus.com/inward/record.url?scp=85062177361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062177361&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619503

DO - 10.1109/CDC.2018.8619503

M3 - Conference contribution

AN - SCOPUS:85062177361

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5940

EP - 5945

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -