In this paper, the input covariance constraint (ICC) control problem is solved by convex optimization subject to linear matrix inequalities (LMIs) constraints. The ICC control problem is an optimal control problem that is concerned to obtain the best output performance subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. Both continuous- and discrete-time problems are considered. To validate our scheme in real-world systems, ICC control based on convex optimization approach was used to control the position of an electronic throttle plate. The controller performance compared experimentally with a well-tuned base-line proportional-integral-derivative (PID) controller. Comparison results showed that not only better performance has been achieved but also the required control energy for the ICC controller is lower than that of the base-line controller.

References

References
1.
Zhu
,
G.
,
Grigoriadis
,
K. M.
, and
Skelton
,
R. E.
,
1995
, “
Covariance Control Design for Hubble Space Telescope
,”
J. Guid., Control, Dyn.
,
18
(
2
), pp.
230
236
.10.2514/3.21374
2.
Christensen
,
R. S.
, and
Geller
,
D.
,
2014
, “
Linear Covariance Techniques for Closed-Loop Guidance Navigation and Control System Design and Analysis
,”
J. Aerosp. Eng.
,
228
(
1
), pp.
44
65
.10.1177/0954410012467717
3.
Kalandros
,
M.
,
2002
, “
Covariance Control for Multisensor Systems
,”
IEEE Trans. Aerosp. Electron. Syst.
,
38
(
4
), pp.
1138
1157
.10.1109/TAES.2002.1145739
4.
Hotz
,
A.
, and
Skelton
,
R. E.
,
1987
, “
Covariance Control Theory
,”
Int. J. Control
,
46
(
1
), pp.
13
32
.10.1080/00207178708933880
5.
Grigoriadis
,
K. M.
, and
Skelton
,
R. E.
,
1997
, “
Minimum-Energy Covariance Controllers
,”
Automatica
,
33
(
4
), pp.
569
578
.10.1016/S0005-1098(96)00188-4
6.
Xu
,
J.
, and
Skelton
,
R.
,
1992
, “
Robust Covariance Control
,”
Robust Control of Lecture Notes in Control and Information Sciences
, Vol.
183
,
Springer
,
Berlin
, pp.
98
105
.
7.
Chen
,
X.
,
Wang
,
Z.
,
Xu
,
G.
,
Guo
,
Z.
, and
Feng
,
Z.
,
1995
, “
Eigenstructure Assignment in State Covariance Control
,”
Syst. Control Lett.
,
26
(
3
), pp.
157
162
.10.1016/0167-6911(95)00008-W
8.
Khaloozadeh
,
H.
, and
Baromand
,
S.
,
2010
, “
State Covariance Assignment Problem
,”
IET Control Theory Appl.
,
4
(
3
), pp.
391
402
.10.1049/iet-cta.2008.0359
9.
Sreeram
,
V.
,
Liu
,
W. Q.
, and
Diab
,
M.
,
1996
, “
Theory of State Covariance Assignment for Linear Single-Input Systems
,”
IEEE Proc. Control Theory Appl.
,
143
(
3
), pp.
289
295
.10.1049/ip-cta:19960242
10.
Hsieh
,
C.
,
Skelton
,
R. E.
, and
Damra
,
F. M.
,
1989
, “
Minimum Energy Controllers With Inequality Constraints on Output Variances
,”
Optim. Control Appl. Methods
,
10
(
4
), pp.
347
366
.10.1002/oca.4660100405
11.
Zhu
,
G.
,
Rotea
,
M.
, and
Skelton
,
R. E.
,
1997
, “
A Convergent Algorithm for the Output Covariance Constraint Control Problem
,”
SIAM J. Control Optim.
,
35
(
1
), pp.
341
361
.10.1137/S0363012994263974
12.
Zhu
,
G.
,
1992
, “
L2 and LMultiobjective Control for Linear Systems
,” Ph.D. thesis, Purdue University, West Lafayette, IN.
13.
Collins
,
E. G.
, Jr.
, and
Selekwa
,
M. F.
,
2002
, “
A Fuzzy Logic Approach to LQG Design With Variance Constraints
,”
IEEE Trans. Control Syst. Technol.
,
10
(
1
), pp.
32
42
.10.1109/87.974336
14.
Conway
,
R.
, and
Horowitz
,
R.
,
2008
, “
A Quasi-Newton Algorithm for LQG Controller Design With Variance Constraints
,”
ASME
Paper No. DSCC2008-2239.10.1115/DSCC2008-2239
15.
White
,
A.
,
Zhu
,
G.
, and
Choi
,
J.
,
2012
, “
A Linear Matrix Inequality Solution to the Output Covariance Constraint Control Problem
,”
ASME
Paper No. DSCC2012-MOVIC2012-8799.10.1115/DSCC2012-MOVIC2012-8799
16.
Al-Jiboory
,
A. K.
,
Zhu
,
G.
, and
Sultan
,
C.
,
2014
, “
LMI Control Design With Input Covariance Constraint for a Tensegrity Simplex Structure
,”
ASME
Paper No. DSCC2014-6122.10.1115/DSCC2014-6122
17.
Nesterov
,
Y.
,
Nemirovskii
,
A.
, and
Ye
,
Y.
,
1994
,
Interior-Point Polynomial Algorithms in Convex Programming
, Vol.
13
,
Society for Industrial and Applied Mathematics (SIAM)
, Philadelphia, PA.
18.
Rotea
,
M. A.
,
1993
, “
The Generalized H2Control Problem
,”
Automatica
,
29
(
2
), pp.
373
385
.10.1016/0005-1098(93)90130-L
19.
De Oliveira
,
M. C.
,
Geromel
,
J. C.
, and
Bernussou
,
J.
,
2002
, “
Extended H2 and H Norm Characterizations and Controller Parameterizations for Discrete-Time Systems
,”
Int. J. Control
,
75
(
9
), pp.
666
679
.10.1080/00207170210140212
20.
Scherer
,
C.
,
Gahinet
,
P.
, and
Chilali
,
M.
,
1997
, “
Multiobjective Output-Feedback Control Via LMI Optimization
,”
IEEE Trans. Autom. Control
,
42
(
7
), pp.
896
911
.10.1109/9.599969
21.
Chilali
,
M.
, and
Gahinet
,
P.
,
1996
, “H
Design With Pole Placement Constraints: An LMI Approach
,”
IEEE Trans. Autom. Control
,
41
(
3
), pp.
358
367
.10.1109/9.486637
22.
Masubuchi
,
I.
,
Ohara
,
A.
, and
Suda
,
N.
,
1998
, “
LMI-Based Controller Synthesis: A Unified Formulation and Solution
,”
Int. J. Rob. Nonlinear Control
,
8
(
8
), pp.
669
686
.10.1002/(SICI)1099-1239(19980715)8:8<669::AID-RNC337>3.0.CO;2-W
23.
De Oliveira
,
M. C.
,
Bernussou
,
J.
, and
Geromel
,
J.
,
1999
, “
A New Discrete-Time Robust Stability Condition
,”
Syst. Control Lett.
,
37
(
4
), pp.
261
265
.10.1016/S0167-6911(99)00035-3
24.
Grepl
,
R.
, and
Lee
,
B.
,
2010
, “
Model Based Controller Design for Automotive Electronic Throttle
,”
Recent Advances in Mechatronics
,
Springer
,
Berlin
, pp.
209
214
.
25.
Zhang
,
S.
,
Yang
,
J. J.
, and
Zhu
,
G. G.
,
2014
, “
LPV Modeling and Mixed Constrained H2/H Control of an Electronic Throttle
,”
IEEE/ASME Trans. Mechatronics
,
PP
(
99
), pp.
1
13
.10.1109/TMECH.2014.2364538
26.
Löfberg
,
J.
,
2004
, “
YALMIP: A Toolbox for Modeling and Optimization in MATLAB
,” IEEE International Symposium on Computer Aided Control Systems Design (
CACSD
), Taipei, Sept. 4, pp.
284
289
.10.1109/CACSD.2004.1393890
27.
Sturm
,
J.
,
1999
, “
Using SeDuMi 1.02, a MATLAB Toolbox for Optimization Over Symmetric Cones
,”
Optim. Methods Software
,
11
(
1
), pp.
625
653
.10.1080/10556789908805766
28.
Keel
,
L.
,
Rego
,
J.
, and
Bhattacharyya
,
S.
,
2003
, “
A New Approach to Digital PID Controller Design
,”
IEEE Trans. Autom. Control
,
48
(
4
), pp.
687
692
.10.1109/TAC.2003.809768
You do not currently have access to this content.