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Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets

Publication ,  Journal Article
Danielson, C; Bridgeman, LJ; Di Cairano, S
Published in: International Journal of Robust and Nonlinear Control
June 2019

This paper studies the control of constrained systems whose dynamics and constraints switch between a finite set of modes over time according to an exogenous input signal. We define a new type of control invariant sets for switched constrained systems, called switch–robust control invariant (switch‐RCI) sets, that are robust to unknown mode switching and exploit available information on minimum dwell‐time and admissible mode transitions. These switch‐RCI sets are used to derive novel necessary and sufficient conditions for the existence of a control‐law that guarantees constraint satisfaction in the presence of unknown mode switching with known minimum dwell‐time. The switch‐RCI sets are also used to design a recursively feasible model predictive controller (MPC) that enforces closed‐loop constraint satisfaction for switched constrained systems. We show that our controller is nonconservative in the sense that it enforces constraints on the largest possible domain, ie, constraints can be recursively satisfied if and only if our controller is feasible. The MPC and switch‐RCI sets are demonstrated on a vehicle lane‐changing case study.

Duke Scholars

Published In

International Journal of Robust and Nonlinear Control

DOI

EISSN

1099-1239

ISSN

1049-8923

Publication Date

June 2019

Volume

29

Issue

9

Start / End Page

2589 / 2602

Publisher

Wiley

Related Subject Headings

  • Industrial Engineering & Automation
  • 4901 Applied mathematics
  • 4009 Electronics, sensors and digital hardware
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
 

Citation

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ICMJE
MLA
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Danielson, C., Bridgeman, L. J., & Di Cairano, S. (2019). Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets. International Journal of Robust and Nonlinear Control, 29(9), 2589–2602. https://doi.org/10.1002/rnc.4509
Danielson, Claus, Leila J. Bridgeman, and Stefano Di Cairano. “Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets.” International Journal of Robust and Nonlinear Control 29, no. 9 (June 2019): 2589–2602. https://doi.org/10.1002/rnc.4509.
Danielson C, Bridgeman LJ, Di Cairano S. Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets. International Journal of Robust and Nonlinear Control. 2019 Jun;29(9):2589–602.
Danielson, Claus, et al. “Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets.” International Journal of Robust and Nonlinear Control, vol. 29, no. 9, Wiley, June 2019, pp. 2589–602. Crossref, doi:10.1002/rnc.4509.
Danielson C, Bridgeman LJ, Di Cairano S. Necessary and sufficient conditions for constraint satisfaction in switched systems using switch‐robust control invariant sets. International Journal of Robust and Nonlinear Control. Wiley; 2019 Jun;29(9):2589–2602.
Journal cover image

Published In

International Journal of Robust and Nonlinear Control

DOI

EISSN

1099-1239

ISSN

1049-8923

Publication Date

June 2019

Volume

29

Issue

9

Start / End Page

2589 / 2602

Publisher

Wiley

Related Subject Headings

  • Industrial Engineering & Automation
  • 4901 Applied mathematics
  • 4009 Electronics, sensors and digital hardware
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics