A dynamic neural network (DNN) observer-based output feedback controller for uncertain nonlinear systems with bounded disturbances is developed. The DNN-based observer works in conjunction with a dynamic filter for state estimation using only output measurements during online operation. A sliding mode term is included in the DNN structure to robustly account for exogenous disturbances and reconstruction errors. Weight update laws for the DNN, based on estimation errors, tracking errors, and the filter output are developed, which guarantee asymptotic regulation of the state estimation error. A combination of a DNN feedforward term, along with the estimated state feedback and sliding mode terms yield an asymptotic tracking result. The developed output feedback (OFB) method yields asymptotic tracking and asymptotic estimation of unmeasurable states for a class of uncertain nonlinear systems with bounded disturbances. A two-link robot manipulator is used to investigate the performance of the proposed control approach.

References

1.
Berghuis
,
H.
, and
Nijmeijer
,
H.
,
1993
, “
A Passivity Approach to Controller-Observer Design for Robots
,”
IEEE Trans. Robot. Autom.
,
9
(
6
), pp.
740
754
.
2.
Do
,
K. D.
,
Jiang
,
Z.
, and
Pan
,
J.
,
2004
, “
A Global Output-Feedback Controller for Simultaneous Tracking and Stabilization for Unicycle-Type Mobile Robots
,”
IEEE Trans. Robot. Autom.
,
20
(
3
), pp.
589
594
.
3.
Lim
,
S. Y.
,
Dawson
,
D. M.
, and
Anderson
,
K.
,
1996
, “
Re-Examining the Nicosia–Tomei Robot Observer-Controller for a Backstepping Perspective
,”
IEEE Trans. Control Syst. Technol.
,
4
(
3
), pp.
304
310
.
4.
Ordaz
,
P.
,
Espinoza
,
E. S.
, and
Munoz
,
F.
,
2014
, “
Global Stability of PD+ Controller With Velocity Estimation
,” 53rd
IEEE
Conference on Decision and Control
, Dec. 15–17, pp.
2585
2590
.
5.
Arteaga
,
M. A.
, and
Kelly
,
R.
,
2004
, “
Robot Control Without Velocity Measurements: New Theory and Experiment Results
,”
IEEE Trans. Robot. Autom.
,
20
(
2
), pp.
297
308
.
6.
Kaneko
,
K.
, and
Horowitz
,
R.
,
1997
, “
Repetitive and Adaptive Control of Robot Manipulators With Velocity Estimation
,”
IEEE Trans. Robot. Autom.
,
13
(
2
), pp.
204
217
.
7.
Burg
,
T.
,
Dawson
,
D. M.
, and
Vedagarbha
,
P.
,
1997
, “
A Redesigned Dcal Controller Without Velocity Measurements: Theory and Demonstration
,”
Robotica
,
15
(
4
), pp.
337
346
.
8.
Kim
,
Y. H.
, and
Lewis
,
F. L.
,
1999
, “
Neural Network Output Feedback Control of Robot Manipulators
,”
IEEE Trans. Robot. Autom.
,
15
(
2
), pp.
301
309
.
9.
Patino
,
H. D.
, and
Liu
,
D.
,
2000
, “
Neural Network-Based Model Reference Adaptive Control System
,”
IEEE Trans. Syst., Man, Cybern., Part B
,
30
(
1
), pp.
198
204
.
10.
Seshagiri
,
S.
, and
Khalil
,
H.
,
2000
, “
Output Feedback Control of Nonlinear Systems Using RBF Neural Networks
,”
IEEE Trans. Neural Network
,
11
(
1
), pp.
69
79
.
11.
Choi
,
J. Y.
, and
Farrell
,
J. A.
,
2001
, “
Adaptive Observer Backstepping Control Using Neural Network
,”
IEEE Trans. Neural Network
,
12
(
5
), pp.
1103
1112
.
12.
Calise
,
A. J.
,
Hovakimyan
,
N.
, and
Idan
,
M.
,
2001
, “
Adaptive Output Feedback Control of Nonlinear Systems Using Neural Networks
,”
Automatica
,
37
(
8
), pp.
1201
1211
.
13.
Hovakimyan
,
N.
,
Nardi
,
F.
,
Calise
,
A.
, and
Kim
,
N.
,
2002
, “
Adaptive Output Feedback Control of Uncertain Nonlinear Systems Using Single-Hidden-Layer Neural Networks
,”
IEEE Trans. Neural Networks
,
13
(
6
), pp.
1420
1431
.
14.
Islam
,
S.
, and
Liu
,
P.
,
2011
, “
Robust Adaptive Fuzzy Output Feedback Control System for Robot Manipulators
,”
IEEE/ASME Trans. Mechatron.
,
16
(
2
), pp.
288
296
.
15.
Xian
,
B.
,
de Queiroz
,
M. S.
,
Dawson
,
D. M.
, and
McIntyre
,
M.
,
2004
, “
A Discontinuous Output Feedback Controller and Velocity Observer for Nonlinear Mechanical Systems
,”
Automatica
,
40
(
4
), pp.
695
700
.
16.
Dinh
,
H. T.
,
Bhasin
,
S.
,
Kim
,
D.
, and
Dixon
,
W. E.
,
2012
, “
Dynamic Neural Network-Based Global Output Feedback Tracking Control for Uncertain Second-Order Nonlinear Systems
,”
American Control Conference
, Montréal, Canada, June 27–29, pp.
6418
6423
.
17.
Polycarpou
,
M.
, and
Ioannou
,
P.
,
1991
, “
Identification and Control of Nonlinear Systems Using Neural Network Models: Design and Stability Analysis
,” Systems Report, University of Southern California, Los Angeles, CA, Tech.
Report No. 91-09-01
.
18.
Hornick
,
K.
,
1991
, “
Approximation Capabilities of Multilayer Feedforward Networks
,”
Neural Networks
,
4
(
2
), pp.
251
257
.
19.
Lewis
,
F. L.
,
Selmic
,
R.
, and
Campos
,
J.
,
2002
,
Neuro-Fuzzy Control of Industrial Systems With Actuator Nonlinearities
,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
.
20.
Funahashi
,
K.
, and
Nakamura
,
Y.
,
1993
, “
Approximation of Dynamic Systems by Continuous-Time Recurrent Neural Networks
,”
Neural Networks
,
6
(
6
), pp.
801
806
.
21.
Gupta
,
M.
,
Jin
,
L.
, and
Homma
,
N.
,
2003
,
Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory
,
Wiley
,
Hoboken, NJ
.
22.
Dixon
,
W. E.
,
Behal
,
A.
,
Dawson
,
D. M.
, and
Nagarkatti
,
S.
,
2003
,
Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach
,
Birkhauser, Boston, MA
.
23.
Krstic
,
M.
,
Kokotovic
,
P. V.
, and
Kanellakopoulos
,
I.
,
1995
,
Nonlinear and Adaptive Control Design
,
Wiley
,
New York
.
24.
Xian
,
B.
,
Dawson
,
D. M.
,
de Queiroz
,
M. S.
, and
Chen
,
J.
,
2004
, “
A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
49
(
7
), pp.
1206
1211
.
25.
Dinh
,
H.
,
Bhasin
,
S.
, and
Dixon
,
W. E.
,
2010
, “
Dynamic Neural Network-Based Robust Identification and Control of a Class of Nonlinear Systems
,”
IEEE
Conference on Decision Control
, Atlanta, GA, Dec. 15–17, pp.
5536
5541
.
26.
Filippov
,
A.
,
1964
, “
Differential Equations With Discontinuous Right-Hand Side
,”
Am. Math. Soc. Transl.
,
42
(
2
), pp.
199
231
.
27.
Filippov
,
A. F.
,
1988
,
Differential Equations With Discontinuous Right-Hand Sides
,
Kluwer Academic Publishers
,
Dordrecht
,
The Netherlands
.
28.
Smirnov
,
G. V.
,
2002
,
Introduction to the Theory of Differential Inclusions
,
Vol. 41, American Mathematical Society
,
Providence, RI
.
29.
Aubin
,
J. P.
, and
Frankowska
,
H.
,
2009
,
Set-Valued Analysis
,
Birkhäuser
,
Boston, MA
.
30.
Clarke
,
F. H.
,
1990
,
Optimization and Nonsmooth Analysis
,
SIAM
,
New York
.
31.
Shevitz
,
D.
, and
Paden
,
B.
,
1994
, “
Lyapunov Stability Theory of Nonsmooth Systems
,”
IEEE Trans. Autom. Control
,
39
(
9
), pp.
1910
1914
.
32.
Paden
,
B.
, and
Sastry
,
S.
,
1987
, “
A Calculus for Computing Filippov’s Differential Inclusion With Application to the Variable Structure Control of Robot Manipulators
,”
IEEE Trans. Circuits Syst.
,
34
(
1
), pp.
73
82
.
33.
Fischer
,
N.
,
Kamalapurkar
,
R.
, and
Dixon
,
W. E.
,
2013
, “
Lasalle-Yoshizawa Corollaries for Nonsmooth Systems
,”
IEEE Trans. Automat. Control
,
58
(
9
), pp.
2333
2338
.
34.
Killingsworth
,
N. J.
, and
Krstic
,
M.
,
2006
, “
PID Tuning Using Extremum Seeking: Online, Model-Free Performance Optimization
,”
IEEE Control Syst. Mag.
,
26
(
1
), pp.
70
79
.
35.
Aström
,
K.
,
Hägglund
,
T.
,
Hang
,
C.
, and
Ho
,
W.
,
1993
, “
Automatic Tuning and Adaptation for PID Controllers—A Survey
,”
Control Eng. Pract.
,
1
(
4
), pp.
669
714
.
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