This paper presents a structurally stable scheme for nonlinear systems which do not satisfy the so-called FIB conditions for the existence of a linear solution to the structurally stable regulator solution, namely, the case when some necessary detectability condition with respect to the original system’s output does not hold. Under certain additional conditions, it is shown that the proposed scheme guarantees zero output tracking error between the actual output and the desired reference signal, in spite of the presence of parameter variations. Application to the model of a rotary inverted pendulum shows the effectiveness of the proposed scheme.

1.
Isidori
,
A.
, 1995,
Nonlinear Control Systems
,
3rd ed.
,
Springer
,
London
.
2.
Isidori
,
A.
, and
Byrnes
,
C. I.
, 1990, “
Output Regulation of Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
35
(
2
), pp.
131
140
.
3.
Francis
,
B. A.
, 1976, “
The Internal Model Principle of Control Theory
,”
Automatica
0005-1098,
12
, pp.
457
465
.
4.
Francis
,
B. A.
, 1977, “
The Linear Multivariable Regulator Problem
,”
SIAM J. Control Optim.
0363-0129,
15
, pp.
486
505
.
5.
Huang
,
J.
, and
Rugh
,
W. J.
, 1990, “
On the Nonlinear Multivariable Servomechanism Problem
,”
Automatica
0005-1098,
26
, pp.
963
972
.
6.
Huang
,
J.
, 2004,
Nonlinear Output Regulation: Theory and Applications
,
SIAM
,
Philadelphia
.
7.
Huang
,
J.
, and
Lin
,
C-F.
, 1993, “
Internal Model Principle and Robust Control of Nonlinear Systems
,” in
Proceedings of the 32nd IEEE CDC
, pp.
1501
1513
.
8.
Hepburn
,
J. S. A.
, and
Wonham
,
W. M.
, 1984, “
Error Feedback and Internal Model on Differentiable Manifolds
,”
IEEE Trans. Autom. Control
0018-9286,
29
, pp.
397
403
.
9.
Byrnes
,
C. I.
,
Delli Priscoli
,
F.
, and
Isidori
,
A.
, 1997,
Output Regulation of Uncertain Nonlinear Systems
,
Birkhauser
,
Boston
.
10.
Huang
,
J.
, 2001, “
Remarks on the Robust Output Regulation Problem for Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
46
(
12
), pp.
2028
2031
.
11.
Huang
,
J.
, 1998, “
K-Fold Exosystem and the Robust Nonlinear Servomechanism Problem
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
120
(
1
), pp.
149
153
.
12.
Huang
,
J.
, and
Chen
,
Z.
, 2004, “
A General Framework for Tackling the Output Regulation Problem
,”
IEEE Trans. Autom. Control
0018-9286,
49
(
12
), pp.
2203
2218
.
13.
Carr
,
J.
, 1981,
Applications of Centre Manifold Theory
,
Springer Verlag
,
New York
.
14.
Castillo-Toledo
,
B.
,
Celikovsky
,
S.
, and
Di Gennaro
,
S.
, 2004, “
Generalized Immersion and Nonlinear Robust Regulation Problem
,”
Kybernetika
0023-5954,
40
(
2
), 2004, pp.
207
220
.
15.
Spong
,
M. W.
, and
Viyasagar
,
M.
, 1989,
Robot Dynamical and Control
,
Wiley
,
New York
.
16.
Knobloch
,
H. W.
,
Isidori
,
A.
, and
Flockerzi
,
D.
, 1993,
Topics in Control Theory
,
Birkhauser Verlag
,
Berlin
.
17.
Castillo-Toledo
,
B.
, 1990, “
Almost Tracking Trough Singular Points via the Nonlinear Regulator Theory
,” in
Proceedings of the IV Latin American Congress on Automatic Control
,
Puebla
,
México
, Vol.
2
, pp.
590
594
.
18.
Huang
,
J.
, and
Rugh
,
W. J.
, 1992, “
An Approximation Method for the Nonlinear Servomechanism Problem
,”
IEEE Trans. Autom. Control
0018-9286,
37
, pp.
1395
1398
.
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