Automatica 46 (2010) 889–896
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Automatica
journal homepage: www.elsevier.com/locate/automatica
Brief paper
Stability and reliable data reconstruction of uncertain dynamic systems over
finite capacity channels
✩
Alireza Farhadi
a,∗
, Charalambos D. Charalambous
b
a
School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada
b
Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia, Cyprus
a r t i c l e i n f o
Article history:
Received 15 March 2009
Received in revised form
22 July 2009
Accepted 5 January 2010
Available online 15 March 2010
Keywords:
Limited capacity
Reconstructability
Robust stability
a b s t r a c t
In this paper we present an encoder, decoder and a stabilizing controller for reliable data reconstruction
and robust stability of uncertain dynamic systems controlled over Additive White Gaussian Noise (AWGN)
channels. The uncertainty in the dynamic system is described by a relative entropy constraint. Such an
uncertainty description is a natural stochastic generalization of the sum quadratic uncertainty description.
This paper complements the results of Farhadi and Charalambous (2008) by showing that the necessary
condition presented there can be tight. This is shown by designing an encoder, decoder and a stabilizing
controller.
© 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Recent development in wireless communication and electron-
ics has given birth to micro-electro-mechanical systems (MEMSs)
which are small in size and communicate in short distances. These
tiny embedded systems, in general, consist of sensors, a data pro-
cessor, a communication unit and an actuator. They are densely
deployed either inside the phenomenon or very close to it. These
embedded systems collaborate with each other by exchanging con-
trol and observation signals via wireless links. However, due to the
limited power of embedded components, the transmission is sub-
ject to limited capacity and noise.
In the above applications, the encoders, decoders and con-
trollers must be designed for real-time communication and control
when the communication is via limited capacity and noisy commu-
nication channels. References Charalambous and Farhadi (2008),
Elia (2004), Farhadi and Charalambous (2008), Li and Baillieul
✩
The research leading to these results has received funding from the European
Community’s Seventh Framework Programme (FP7/2007-2013) under grant
agreement no. INFSO-ICT-223844 and the Cyprus Research Promotion Foundation
under the project ARTEMIS. The material in this paper was partially presented
in the Proceedings of the 2008 American Control Conference. This paper was
recommended for publication in revised form by Associate Editor George Yin under
the direction of Editor Ian R. Petersen. The authors would like to thank Professor
N.U. Ahmed for many helpful discussions.
∗
Corresponding author. Tel.: +357 22892253; fax: +357 22892260.
E-mail addresses: afarhadi@alumni.uottawa.ca (A. Farhadi), chadcha@ucy.ac.cy
(C.D. Charalambous).
(2004), Liberzon and Hespanha (2005), Martins, Dahleh, and Elia
(2006), Malyavej and Savkin (2005), Matveev and Savkin (2007),
Nair and Evans (2004), Nair, Evans, Mareels, and Moran (2004),
Savkin and Petersen (2003), Tatikonda, Sahai, and Mitter (2004)
and Yuksel and Basar (2007) are representative although not ex-
haustive of the recent activity addressing the above questions.
They present necessary and sufficient conditions for the stabil-
ity and reliable data reconstruction of dynamic systems. However,
most of these publications are concerned with cases when the
dynamic model and communication channel are known. In prac-
tice, uncertain dynamic systems and channels are more realistic
representations of the actual problems. Only in few publications
(e.g., Martins et al., 2006; Matveev & Savkin, 2007) uncertain dy-
namic systems are considered, in which the uncertain dynamic sys-
tems are subject to uniformly bounded disturbances. This excludes
dynamic systems which are subject to deterministic or stochastic
disturbances of finite energy or power, which are often dealt with
using minimax techniques.
This paper addresses control over limited capacity for a class of
dynamic systems described by a relative entropy constraint. Such
an uncertainty description is a generalization of the sum quadratic
uncertainty description considered in Moheimani, Savkin, and
Petersen (1995) and Petersen and James (1996). The sum
quadratic uncertainty description includes the uniformly bounded
uncertainty description as a special case. Consequently, this paper
complements the results of Farhadi and Charalambous (2008) by
presenting an encoder, a decoder and a controller for uniform
reliable data reconstruction and robust stability of an uncertain
dynamic system subject to the relative entropy constraint, when it
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doi:10.1016/j.automatica.2010.02.002