This paper considers a novel coupled state-dependent Riccati equation (SDRE) approach for systematically designing nonlinear quadratic regulator (NLQR) and H control of mechatronics systems. The state-dependent feedback control solutions can be obtained by solving a pair of coupled SDREs, guaranteeing nonlinear quadratic optimality with inherent stability property in combination with robust L2 type of disturbance reduction. The derivation of this control strategy is based on Nash's game theory. Both finite and infinite horizon control problems are discussed. An under-actuated robotic system, Furuta rotary pendulum, is used to examine the effectiveness and robustness of this novel nonlinear control approach.

References

References
1.
Isidori
,
A.
,
1995
,
Nonlinear Control Systems
,
3rd ed.
,
Springer
, London.
2.
Utkin
,
V. I.
,
1993
, “
Sliding Mode Control Design Principles and Applications to Electric Drives
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
23
36
.
3.
Hostettler
,
J.
, and
Wang
,
X.
,
2015
, “
Sliding Mode Control of A Permanent Magnet Synchronous Generator for Variable Speed Wind Energy Conversion Systems
,”
American Control Conference
, Chicago, IL, July 1–3, pp.
4982
4987
.
4.
Slotine
,
J.-J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
Englewood Cliffs, NJ
.
5.
Tao
,
G.
,
2004
,
Adaptive Control Design and Analysis
,
Wiley
, Hoboken, NJ.
6.
Sun
,
W.
,
Pan
,
H.
, and
Gao
,
H.
,
2016
, “
Filter-Based Adaptive Vibration Control for Active Vehicle Suspensions With Electrohydraulic Actuators
,”
IEEE Trans. Veh. Technol.
,
65
(
6
), pp.
4619
4626
.
7.
Pan
,
H.
,
Sun
,
W.
,
Gao
,
H.
, and
Yu
,
J.
,
2015
, “
Finite-Time Stabilization for Vehicle Active Suspension Systems With Hard Constraints
,”
IEEE Trans. Intell. Transportation Syst.
,
16
(
5
), pp.
2663
2672
.
8.
Pan
,
H.
,
Sun
,
W.
,
Gao
,
H.
, and
Jing
,
X.
,
2016
, “
Disturbance Observer-Based Adaptive Tracking Control With Actuator Saturation and Its Application
,”
IEEE Trans. Autom. Sci. Eng.
,
13
(
2
), pp.
868
875
.
9.
Van der Shaft
,
A. J.
,
1993
, “
Nonlinear State Space H∞ Control Theory
,”
Birkhauser Perspectives in Control
,
H. J.
Trentelman
and
J. C.
Willems
, eds., Birkhauser, Boston, MA.
10.
Doyle
,
J. H.
,
Glover
,
K.
,
Khargonekar
,
P.
, and
Francis
,
B.
,
1989
, “
State Solution to Standard H2 and H∞ Control Problems
,”
IEEE Trans. Autom. Control
,
3
, pp.
831
847
.
11.
Glover
,
K.
, and
Doyle
,
J. C.
,
1989
, “
A State Space Approach to H-Infinity Optimal Control
,”
Three Decades of Mathematical System Theory
,
H
.
Nijmeijer
and
J. M.
Schumacher
, eds.,
Springer-Verlag
,
Berlin
, pp.
179
218
.
12.
Bernstein
,
D. S.
, and
Haddad
,
W. M.
,
1989
, “
LQG Control With an H∞ Performance Bound: A Riccati Equation Approach
,”
IEEE Trans. Autom. Control
,
34
(
3
), pp.
293
305
.
13.
Doyle
,
J.
,
Zhou
,
K.
,
Glover
,
K.
, and
Bodenheimer
,
B.
,
1994
, “
Mixed H2 and H∞ Performance Objectives—II: Optimal Control
,”
IEEE Trans. Autom. Control
,
39
(
8
), pp.
1575
1587
.
14.
Iglesias
,
P. A.
,
Mustafa
,
D.
, and
Glover
,
K.
,
1990
, “
Discrete Time H∞ Controllers Satisfying a Minimum Entropy Criterion
,”
Syst. Control Lett.
,
14
(
4
), pp.
275
286
.
15.
Mustafa
,
D.
, and
Glover
,
K.
,
1990
,
Minimum Entropy H∞ Control
(Lecture Notes in Control and Information Sciences, Vol.
146
),
Springer
,
Berlin
.
16.
Khargonekar
,
P. P.
, and
Rotea
,
M. A.
,
1991
, “
Mixed H2-H∞ Control: A Convex Optimization Approach
,”
IEEE Trans. Autom. Control
,
36
(
7
), pp.
824
837
.
17.
Scherer
,
C. W.
,
1995
, “
Multi-Objective H2-H∞ Control
,”
IEEE Trans. Autom. Control
,
40
(
6
), pp.
1054
1062
.
18.
D. J. N.
,
Limebeer
,
B. D. O.
,
Anderson
,
B.
, and
Hendel
,
A.
,
1994
, “
Nash Game Approach to the Mixed H2-H∞-Control Problem
,”
IEEE Trans. Autom. Control
,
39
(
1
), pp.
824
839
.
19.
Basar
,
T.
, and
Bernhard
,
P.
,
1995
,
H∞ Optimal Control and Related Minimax Design Problems — A Dynamic Game Approach
,
2nd ed.
,
Birkhauser
, Boston, MA.
20.
Chen
,
X.
, and
Zhou
,
K.
,
2001
, “
Multi-Objective H2-H∞-Control Design
,”
SIAM J. Control Optim.
,
40
(
2
), pp.
628
660
.
21.
Lin
,
W.
,
1996
, “
Mixed H2-H∞-Control for Nonlinear Systems
,”
Int. J. Control
,
64
(
5
), pp.
899
922
.
22.
Lin
,
W.
,
1995
, “
Mixed H2-H∞-Control for Nonlinear Systems
,”
34th IEEE Conference on Decision and Control
, New Orleans, LA, Dec. 13–15, pp. 333–338.
23.
Lin
,
W.
, and
Byrnes
,
C. I.
,
1994
, “
Dissipativity, L2-Gain and H∞-Control for Discrete-Time Nonlinear Systems
,”
American Control Conference
, Baltimore, MD, June 29–July 1, pp.
2257
2260
.
24.
Lin
,
W.
, and
Byrnes
,
C. I.
,
1996
, “
H∞-Control of Discrete-Time Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
41
(
4
), pp.
494
509
.
25.
Lin
,
W.
, and
Byrnes
,
C. I.
,
1995
, “
Discrete-Time Nonlinear H∞ Control With Measurement Feedback
,”
Automatica
,
31
(
3
), pp.
419
434
.
26.
Huang
,
Y.
, and
Lu
,
W.-M.
,
1996
, “
Nonlinear Optimal Control: Alternatives to Hamilton-Jacobi Equation
,”
35th Conference on Decision and Control
(
CDC
), Kobe, Japan, Dec. 13, pp.
3942
3947
.
27.
Wang
,
X.
,
Yaz
,
E. E.
, and
Yaz
,
Y. I.
,
2010
, “
Robust and Resilient State Dependent Control of Continuous Time Nonlinear Systems With General Performance Criteria
,”
49th IEEE Conference on Decision and Control
(
CDC
), Atlanta, GA, Dec. 15–17, pp. 603–608.
28.
Wang
,
X.
,
Yaz
,
E. E.
, and
Yaz
,
Y. I.
,
2011
, “
Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems With General Performance Criteria
,”
18th IFAC World Congress
, Milano, Italy, Aug. 28–Sept. 2, pp.
10904
10909
.
29.
Cloutier
,
J. R.
,
D'Souza
,
C. N.
, and
Mracek
,
C. P.
,
1996
, “
Nonlinear Regulation and Nonlinear Control Via the State-Dependent Riccati Equation Technique—Part 1: Theory, Part 2 Examples
,”
First International Conference on Nonlinear Problems in Aviation and Aerospace,
Daytona Beach, FL, May 9–11, pp.
117
141
.
30.
Cloutier
,
J. R.
,
1997
, “
State-Dependent Riccati Equation Techniques: An Overview
,”
American Control Conference
(
ACC
), Albuquerque, MN, June 6, pp.
932
936
.
31.
Dutka
,
A. S.
,
Ordys
,
A. W.
, and
Grimble
,
M. J.
,
2005
, “
Optimized Discrete-Time State Dependent Riccati Equation Regulator
,”
American Control Conference
(
ACC
), Portland, OR, June 8–10, pp.
2293
2298
.
32.
Cimen
,
T.
,
2008
, “
State Dependent Riccati Equation (SDRE) Control: A Survey
,”
17th World Congress, the International Federation of Automatic Control
, Seoul, Korea, July 6–11, pp.
3761
3775
.
33.
Wang
,
X.
,
Yaz
,
E. E.
,
Schneider
,
S. C.
, and
Yaz
,
Y. I.
, Oct.
2011
, “
H2-H∞ Control of Discrete Time Nonlinear Systems Using SDRE Approach
,”
ASME
Paper No. DSCC2011-5935.
34.
Aliyu
,
M. D. S.
,
2011
,
Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations
,
CRC Press
, Boca Raton, FL.
35.
Izutsu
,
M.
,
Pan
,
Y.
, and
Furuta
,
K.
, Jan.
2008
, “
Swing-Up of Furuta Pendulum by Nonlinear Sliding Mode Control
,”
SICE J. Control, Meas., Syst. Integration
,
1
(
1
), pp.
12
17
.
36.
Hernández-Guzmán
,
V. M.
,
Antonio-Cruz
,
M.
, and
Silva-Ortigoza
,
R.
,
2016
, “
Linear State Feedback Regulation of a Furuta Pendulum: Design Based on Differential Flatness and Root Locus
,”
IEEE Access
,
4
, pp.
8721
8736
.
You do not currently have access to this content.