In this paper sliding mode surface design is concerned with multi objective optimization for nonlinear continuous-time systems in the presence of matched and mismatched uncertainties and disturbances. In order to reduce the effect of uncertainties and disturbances on sliding motion, this problem is formulated as a well-motivated mixed H2/H optimization problem and a constructive algorithm based on linear matrix inequality (LMI) is proposed. We also give an LMI-based sliding mode control law to direct the system trajectories onto the designed sliding surface. Finally, using a numerical example, we show the effectiveness of proposed method.

References

References
1.
Takahashi
,
R. H. C.
, and
Peres
,
P. L. D.
,
1999
, “H2
Guaranteed Cost Switching Surface Design for Sliding Modes With Nonmatching Disturbances
,”
IEEE Trans. Autom. Control
,
44
, pp.
2214
2218
.10.1109/9.802948
2.
Gouaisbaut
,
F.
,
Dambrine
,
M.
, and
Richard
,
J. P.
,
2002
, “
Robust Control of Delay Systems: A Sliding Mode Control Design Via LMI
,”
Syst. Control Lett.
,
46
(
4
), pp.
219
230
.10.1016/S0167-6911(01)00199-2
3.
Choi
,
H. H.
,
2003
, “
An LMI-Based Switching Surface Design Method for a Class of Mismatched Uncertain Systems
,”
IEEE Trans. Autom. Control
,
48
, pp.
1634
1638
.10.1109/TAC.2003.817007
4.
Edwards
,
C. A.
,
2004
, “
A Practical Method for the Design of Sliding Mode Controllers Using Linear Matrix Inequalities
,”
Automatica
,
40
, pp.
1761
1769
.10.1016/j.automatica.2004.05.004
5.
Edwards
,
C.
,
Fossas Colet
,
E.
, and
Fridman
,
L. E.
,
2006
,
Advances in Variable Structure and Sliding Mode Control
,
Springer–Verlag
,
Berlin
.
6.
Choi
,
H. H.
,
2007
, “
LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems
,”
IEEE Trans. Autom. Control
,
52
, pp.
736
742
.10.1109/TAC.2007.894543
7.
Park
,
P.
,
Choi
,
D. J.
, and
Kong
,
S. G.
,
2007
, “
Output Feedback Variable Structure Control for Linear Systems With Uncertainties and Disturbances
,”
Automatica
,
43
, pp.
72
79
.10.1016/j.automatica.2006.07.015
8.
Wang
,
H.
,
Han
,
Z. Z.
,
Xie
,
Q. Y.
, and
Zhang
,
W.
,
2009
, “
Sliding Mode Control for Chaotic Systems Based on LMI
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
4
), pp.
1410
1417
.10.1016/j.cnsns.2007.12.006
9.
Wua
,
L.
,
Sua
,
X.
, and
Shib
,
P.
,
2012
, “
Sliding Mode Control With Bounded L2 Gain Performance of Markovian Jump Singular Time-Delay Systems
,”
Automatica
,
48
(
8
), pp.
1929
1933
.10.1016/j.automatica.2012.05.064
10.
Guo
,
B. Z.
, and
Liu
,
J. J.
,
2013
, “
Sliding Mode Control and Active Disturbance Rejection Control to the Stabilization of One-Dimensional Schrödinger Equation Subject to Boundary Control Matched Disturbance
,”
Int. J. Robust Nonlinear Control
,
23
(
8
), pp.
1012
1018
.10.1002/rnc.1843
11.
Sarvi
,
M.
,
Soltani
,
I.
,
Namazy Pour
,
N.
, and
Rabbani
,
N.
,
2013
, “
A New Sliding Mode Controller for DC/DC Converters in Photovoltaic Systems
,”
J. Energy
,
13
(
13
), pp.
801
808
.10.1155/2013/871025
12.
EL-Ghezawi
,
O. M. E.
,
Zinober
,
A. S. I.
, and
Billings
,
A. A.
,
1983
, “
Analysis and Design of Variable Structure Systems Using a Geometric Approach
,”
Int. J. Control
,
38
, pp.
657
671
.10.1080/00207178308933100
13.
Dorling
,
C. M.
, and
Zinober
,
S. I.
,
1989
, “
Two Approaches to Hyperplane Design in Multivariable Structure Control Systems
,”
Int. J. Control
,
44
, pp.
65
82
.10.1080/00207178608933583
14.
Choi
,
H. H.
,
2008
, “
Output Feedback Variable Structure Control Design With an H2 Performance Bound Constraint
,”
Automatica
,
44
, pp.
2403
2408
.10.1016/j.automatica.2008.01.018
15.
Castanos
,
F.
, and
Fridman
,
L.
,
2006
, “
Analysis and Design of Integral Sliding Manifolds for Systems With Unmatched Perturbations
,”
IEEE Trans. Autom. Control
,
51
, pp.
853
858
.10.1109/TAC.2006.875008
16.
Kim
,
K. S.
, and
Park
,
Y.
,
2000
, “
Using Lyapunov Matrices for Sliding Mode Design
,”
Proceedings of the 39th Conference on Decision and Control
, pp.
2204
2209
.
17.
Kim
,
K. S.
, and
Park
,
Y.
,
2004
, “
Sliding Mode Design Via Quadratic Performance Optimization With Pole-Clustering Constraint
,”
SIAM J. Control Optim.
,
43
, pp.
670
684
.10.1137/S0363012901388476
18.
Khargonekar
,
P. P.
, and
Rotea
,
M. A.
,
1991
, “
Mixed H2/H Control: A Convex Optimization Approach
,”
IEEE Trans. Autom. Control
,
36
, pp.
824
837
.10.1109/9.85062
19.
Scherer
,
C. W.
,
Gahinet
,
P.
, and
Chilali
,
M.
,
1997
, “
Multi-Objective Output Feedback Control
,”
IEEE Trans. Autom. Control
,
17
, pp.
138
149
.
20.
Khosrowjerdi
,
M. J.
,
Nikoukhah
,
R.
, and
Safari-Shad
,
N.
,
2004
, “
A Mixed H2/H Approach to Simultaneous Fault Detection and Control
,”
Automatica
,
40
, pp.
261
267
.10.1016/j.automatica.2003.09.011
21.
Scherer
,
C.
, and
Weiland
S.
,
1999
, Lecture Notes DISC Course on Linear Matrix Inequalities in Control,
Delft University of Technology
,
Delft, The Netherlands
, p.
54
.
22.
Boyd
,
S.
,
El Ghaoui
,
L.
,
Feron
,
E.
, and
Balakrishnan
,
V.
,
1994
, Linear Matrix Inequalities in System and Control Theory, “
Studies in Applied Mathematics
,” Vol.
15
,
SIAM
,
Philadelphia, PA
, p.
28
.
23.
Khargonekar
,
P. P.
,
Petersen
,
I. R.
, and
Zhou
,
K.
,
1990
, “
Robust Stabilization of Uncertain Linear Systems: Quadratic Stabilizability and H Control Theory
,”
IEEE Trans. Autom. Control
,
35
, pp.
356
361
.10.1109/9.50357
24.
Wang
,
Y.
,
Xie
,
L.
, and
deSousa
,
C. E.
,
1992
, “
Robust Control of a Class of Uncertain Nonlinear Systems
,”
Syst. Control Lett.
,
19
, pp.
139
149
.10.1016/0167-6911(92)90097-C
25.
Bernstein
,
D. S.
, and
Haddad
,
W. M.
,
1989
, “
LQG Control With an H Performance Bound: A Riccati Equation Approach
,”
IEEE Trans. Autom. Control
,
34
, pp.
293
305
.10.1109/9.16419
26.
Castanos
,
F.
, and
Fridman
,
L.
,
2011
, “
Dynamic Switching Surfaces for Output Sliding Mode Control: An H Approach
,”
Automatica
,
47
, pp.
1957
1961
.10.1016/j.automatica.2011.05.012
27.
Gahinet
,
P.
,
Nemirovski
,
A.
,
Laub
,
A. J.
, and
Chilali
,
M.
,
1995
,
LMI Control Toolbox
,
The Math Works
,
Natick, MA
.
28.
El Ghaoui
,
L.
,
Nikoukhah
,
R.
,
Delebecque
,
F.
, and
Commeau
,
J. L.
,
1998
, “
LMITOOL-2.0 Package: An Interface to Solve LMI Problems
,”
Optimization and Control Group
,
ENSTA
,
Paris, France
.
You do not currently have access to this content.