Observer-based control of linear complementarity systems

W.P.M.H. Heemels, M.K. Camlibel, J.M. Schumacher, B. Brogliato

Research output: Contribution to journalArticleScientificpeer-review

297 Downloads (Pure)

Abstract

In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed-loop system is well-posed and globally exponentially stable. In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented.
Original languageEnglish
Pages (from-to)1193-1218
JournalInternational Journal of Robust and Nonlinear Control
Volume21
Issue number10
DOIs
Publication statusPublished - 2011

Fingerprint

Linear systems
Asymptotic stability
State feedback
Closed loop systems
Dynamical systems
Stabilization
Trajectories
Controllers

Cite this

Heemels, W. P. M. H., Camlibel, M. K., Schumacher, J. M., & Brogliato, B. (2011). Observer-based control of linear complementarity systems. International Journal of Robust and Nonlinear Control, 21(10), 1193-1218. https://doi.org/10.1002/rnc.1626
Heemels, W.P.M.H. ; Camlibel, M.K. ; Schumacher, J.M. ; Brogliato, B. / Observer-based control of linear complementarity systems. In: International Journal of Robust and Nonlinear Control. 2011 ; Vol. 21, No. 10. pp. 1193-1218.
@article{38b3325c4d334c2f92f896ab7d4e7d79,
title = "Observer-based control of linear complementarity systems",
abstract = "In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed-loop system is well-posed and globally exponentially stable. In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented.",
author = "W.P.M.H. Heemels and M.K. Camlibel and J.M. Schumacher and B. Brogliato",
year = "2011",
doi = "10.1002/rnc.1626",
language = "English",
volume = "21",
pages = "1193--1218",
journal = "International Journal of Robust and Nonlinear Control",
issn = "1049-8923",
publisher = "John Wiley and Sons Ltd",
number = "10",

}

Heemels, WPMH, Camlibel, MK, Schumacher, JM & Brogliato, B 2011, 'Observer-based control of linear complementarity systems', International Journal of Robust and Nonlinear Control, vol. 21, no. 10, pp. 1193-1218. https://doi.org/10.1002/rnc.1626

Observer-based control of linear complementarity systems. / Heemels, W.P.M.H.; Camlibel, M.K.; Schumacher, J.M.; Brogliato, B.

In: International Journal of Robust and Nonlinear Control, Vol. 21, No. 10, 2011, p. 1193-1218.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Observer-based control of linear complementarity systems

AU - Heemels, W.P.M.H.

AU - Camlibel, M.K.

AU - Schumacher, J.M.

AU - Brogliato, B.

PY - 2011

Y1 - 2011

N2 - In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed-loop system is well-posed and globally exponentially stable. In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented.

AB - In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS. In particular, we present an observer design method for LCS which is effective even in the presence of state jumps. We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error. These two properties guarantee that the estimated state exponentially recovers the state of the system. For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer. We prove that the resulting closed-loop system is well-posed and globally exponentially stable. In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented.

U2 - 10.1002/rnc.1626

DO - 10.1002/rnc.1626

M3 - Article

VL - 21

SP - 1193

EP - 1218

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1049-8923

IS - 10

ER -