This paper addresses the problem of optimal control and scheduling of Networked Control Systems over limited bandwidth deterministic networks using some insight on the interplay between the control and information theory. The motivation is related to the necessity of choice a communication sequence which maximize control signal impact on the plant behavior. The solution is obtained by decomposing the overall problem in a twofold one. The first level problem aims obtaining the periodic off-line or static scheduling function of control signals based on system properties, communication constrains, periodicity of scheduling sequence, performance criteria and maximization of the degree of reachability/observability of the periodic system. A Mixed Integer Quadratic Programming (MIQP) problem is formulated and solved obtaining a periodic and stable NCS. The solution of the second level problem is based on the structure of the static scheduling function obtained from the first level solution and the dependance of the degree of reachability/observability on the current state of the system.

References

References
1.
Abdallah
,
Ch
Mathematical controllability of genomic networks
. In
Proc. of the National Academy of Science of The United States of America, October
2011
.
2.
Antoulas
,
A.
Approximation of Large-Scale Dynamical Systems. SIAM
,
2005
.
3.
Arzen
,
K.E.
Cervin
,
A.
Eker
,
J.
and
Sha
,
L.
An introduction to control and real-time scheduling co-design.
In
Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December
2000
.
4.
Ben Gaid
,
A.
and
Cela
,
A.
Trading quantization precision for sampling rates in networked systems with limited communication.
In
Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA., Dec.
2006
.
5.
Ben Gaid
,
M.
,
Cela
,
A.
, and
Hamam
,
Y.
Optimal integrated control and scheduling of networked control systems with communication constraints: Application to a car suspension system
.
IEEE Transactions on Control Systems Technology
,
14
(4)
, July
2006
.
6.
Brockett
,
R.W.
Finite Dimensional Linear Systems
.
Wiley
,
New York, USA
,
1970
.
7.
Cervin
,
Anton
Eker
,
Johan
,
Bernhardsson
,
Bo
, and
Arzen
,
Karl-Erik
.
Feedback-feedforward scheduling of control tasks
.
Real-Time Systems
,
23
(1)
:
25
{
53
, July
2002
.
8.
Hristu
,
D.
Optimal control with limited communication. PhD thesis, Division of Engineering and Applied Sciences, Harvard University
, June
1999
.
9.
Iglesias
,
P.
Trade-os in linear time-varying systems: An analogue of Bode's sensitivity integral. Automatica
,
37
(10)
:
1541
{
1550
,
2001
.
10.
Prateep Roy
,
Kumar
.
Analysis and Design of Distributed Embedded Systems under Communication Constraints. PhD thesis, EPE, ESIEE Paris, Embeded System Department
, December
2009
.
11.
Lee
,
K.C.
,
Lee
,
S.
, and
Lee
,
M.H.
Qos-based remote control of networked control systems via probus token passing protocol
.
IEEE Transactions on Industrial Informatics
,
1
(3)
:
183
{
191
,
2005
.
12.
Mart
,
P.
,
Yepez
,
J.
,
Velasco
,
M.
,
Villa
,
R.
, and
Fuertes
,
J.M.
Managing quality-of-control in network-based control systems by controller and message scheduling co-design
.
IEEE Transactions on Industrial Electronics
,
51
(6)
:
1159
{
1167
,
2004
.
13.
Mehta
,
P.
,
Vaidya
,
U.
, and
Banaszuk
,
A.
Markov chains, entropy, and fundamental limitations in nonlinear stabilization
. In
Proc. of the 45th IEEE Conference on Decision & Control, San Diego, US
A, December
13
15
2006
.
14.
Mitra
,
D.
W-matrix and the geometry of model equivalence and reduction
.
Proc. of the IEE
,
116
(6)
:
1101
{
1106
, June
1969
.
15.
Moore
,
B.
Principal component analysis in linear systems: Controllability, observability, and model reduction
. In
IEEE Transaction on Automatic Control, volume AC-26, New Orleans, LA, USA, February
1981
.
16.
Nair
,
G.
and
Evans
,
R.
Stabilizability of stochastic linear systems with nite feedback data rates
.
SIAM J. Control Optim
.,
43
(2)
:
413
{
436
, December
2004
.
17.
Okano
,
K.
,
Hara
,
S.
, and
Ishii
,
H.
Characterization of a complementary sensitivity property in feedback control: An information theoretic approach
. In
Proc. of the 17th IFAC-World Congress, Seoul, Korea
, July
6
{
11
2008
.
18.
Rugh
,
W.J.
Linear System Theory. Prentice Hall
,
1996
.
19.
Tatikonda
,
S.
and
Mitter
,
S.
Control under communication constraints
.
IEEE Trans. Autom. Control
,
49
(7)
:
1056
{
1068
, July
2004
.
20.
Theeranaew
,
W.
Study on Information Theory: Connection to Control Theory, Approach and Analysis for Computation. PhD thesis, Department of Electrical Engineering and Computer Science,CWE University, January
2015
.
21.
B.
,
B.
and
Jonckheere
,
E.
,
A simplied approach to Bode's theorem for continuous-time and discrete-time systems
.
IEEE Transactions on Automatic Control
,
37
(11)
, November
1992
.
22.
Zang
,
G.
. and
Iglesias
,
P.
Nonlinear extension of Bode's integral based on an information theoretic interpretation.
Systems and Control Letters
,
50
:
11
{
29
,
2003
.
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