This paper considers the stabilization problem of a continuous linear system over a communication channel with network-induced delay. The channel is of finite data rate and connects the measurement sensor to the controller. Based on spherical polar coordinates, a novel coding scheme is proposed for this problem. In this coding scheme, the quantizer does not quantize the state of the original quantized system directly, but quantizes the state of the corresponding augmented system to produce control inputs, which simplifies the design of the coding scheme; a definite relation between the quantized data and the corresponding quantization error is used to facilitate the analysis of the stability of the system. Based on this coding scheme, the paper presents the condition guaranteeing the asymptotic stability of the system with network-induced delay and gives the design procedure of quantizer and controller. It is shown that adopting spherical polar coordinates makes the practical solving for the parameters of the quantizer and the controller numerically realistic.

References

References
1.
Tatikonda
,
S.
, and
Mitter
,
S.
,
2004
, “
Control Under Communication Constraints
,”
IEEE Trans. Autom.
,
49
(
7
), pp.
1056
1068
.
2.
Matveev
,
A. S.
, and
Savkin
,
A. V.
,
2009
,
Estimation and Control Over Communication Networks
(Control Engineering),
Birkhauser
,
Boston
.
3.
Elia
,
N.
, and
Mitter
,
S. K.
,
2009
, “
Stabilization of Linear Systems With Limited Information
,”
IEEE Trans. Autom. Control
,
46
(
9
), pp.
1384
1400
.
4.
Ling
,
Q.
, and
Lemmon
,
M. D.
,
2005
, “
Stability of Quantized Control Systems Under Dynamic Bit Assignment
,”
IEEE Trans. Autom. Control
,
50
(
5
), pp.
734
740
.
5.
Savkin
,
A. V.
,
2006
, “
Analysis and Synthesis of Networked Control Systems: Topological Entropy, Observability, Robustness, and Optimal Control
,”
Automatica
,
42
(
1
), pp.
51
62
.
6.
Freudenberg
,
J.
,
Braslavsky
,
J.
, and
Middleton
,
R.
,
2005
, “
Control Over Signal-to-Noise Ratio Constrained Channels: Stabilization and Performance
,”
44th IEEE Conference on Decision and Control and 2005 European Control Conference
, Seville, Spain, Dec. 12–15, pp.
191
196
.
7.
Martins
,
N. C.
, and
Dahleh
,
M. A.
,
2008
, “
Feedback Control in the Presence of Noisy Channels: ‘Bode-Like’ Fundamental Limitations of Performance
,”
IEEE Trans. Autom. Control
,
53
(
7
), pp.
1604
1614
.
8.
Wong
,
W. S.
, and
Brockett
,
R. W.
,
1999
, “
Systems With Finite Communication Bandwidth Constraints II: Stabilization With Limited Information Feedback
,”
IEEE Trans. Autom. Control
,
44
(
7
), pp.
1049
1053
.
9.
Li
,
K.
, and
Baillieul
,
J.
,
2004
, “
Robust Quantization for Digital Finite Communication Bandwidth (DFCB) Control
,”
IEEE Trans. Autom. Control
,
49
(
9
), pp.
1573
1584
.
10.
Fagnani
,
F.
, and
Zampieri
,
S.
,
2005
, “
A Symbolic Approach to Performance Analysis of Quantized Feedback Systems: The Scalar Case
,”
SIAM J. Control Optim.
,
44
(
3
), pp.
816
866
.
11.
Nair
,
G. N.
,
Fagnani
,
F.
,
Zampieri
,
S.
, and
Evans
,
R. J.
,
2007
, “
Feedback Control Under Data Rate Constraints: An Overview
,”
Proc. IEEE
,
95
(
1
), pp.
108
137
.
12.
Brockett
,
R. W.
, and
Liberzon
,
D.
,
2000
, “
Quantized Feedback Stabilization of Linear Systems
,”
IEEE Trans. Autom. Control
,
45
(
7
), pp.
1279
1289
.
13.
Jaglin
,
J.
,
de Wit
,
C. C.
, and
Siclet
,
C.
,
2008
, “
Delta Modulation for Multivariable Centralized Linear Networked Controlled Systems
,”
47th IEEE Conference on Decision and Control
, Cancun, Mexico, Dec. 9–11, pp.
4910
4915
.
14.
Sharon
,
Y.
, and
Liberzon
,
D.
,
2007
, “
Input-to-State Stabilization With Minimum Number of Quantization Regions
,”
46th IEEE Conference on Decision and Control
, New Orleans, LA, Dec. 12–14, pp.
20
25
.
15.
Wang
,
J.
, and
Yan
,
Z.
,
2014
, “
Coding Scheme Based on Spherical Polar Coordinate for Control Over Packet Erasure Channel
,”
Int. J. Robust Nonlinear Control
,
24
(
7
), pp.
1159
1176
.
16.
Sinopoli
,
B.
,
Goldsmith
,
A.
,
Casavola
,
A.
, and
Garone
,
E.
,
2012
, “
LQG Control for MIMO Systems Over Multiple Erasure Channels With Perfect Acknowledgment
,”
IEEE Trans. Autom. Control
,
57
(
2
), pp.
450
456
.
17.
Gupta
,
V.
,
Spanos
,
D.
,
Hassibi
,
B.
, and
Murray
,
R. M.
,
2007
, “
Optimal LQG Control Across a Packet-Dropping Link
,”
Syst. Control Lett.
,
56
(
6
), pp.
439
446
.
18.
Elia
,
N.
,
2005
, “
Remote Stabilization Over Fading Channels
,”
Syst. Control Lett.
,
54
(
3
), pp.
237
249
.
19.
Diwadkar
,
A.
, and
Vaidya
,
U.
,
2014
, “
Stabilization of Linear Time Varying Systems Over Uncertain Channels
,”
Int. J. Robust Nonlinear Control
,
24
(
7
), pp.
1205
1220
.
20.
Li
,
L.
,
Wang
,
X.
, and
Lemmon
,
M.
,
2012
, “
Stabilizing Bit-Rates in Quantized Event Triggered Control Systems
,”
15th ACM International Conference on Hybrid Systems: Computation and Control
, Beijing, China, Apr. 17–19, pp.
245
254
.
21.
Sun
,
Y.
, and
Wang
,
X.
,
2014
, “
Stabilizing Bit-Rates in Networked Control Systems With Decentralized Event-Triggered Communication
,”
Discrete Event Dyn. Syst.
,
24
(
2
), pp.
219
245
.
22.
Horn
,
R. A.
, and
Johnson
,
C. R.
,
1986
,
Matrix Analysis
, Vol.
1
,
Cambridge University Press
,
Cambridge, UK
.
23.
Hetel
,
L.
,
Daafouz
,
J.
, and
Iung
,
C.
,
2006
, “
Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays
,”
IEEE Trans. Autom. Control
,
51
(
10
), pp.
1668
1671
.
You do not currently have access to this content.