This paper presents a new recursive forwarding method to design control laws that globally asymptotically stabilize strict-feedforward systems, of which Jacobian linearization at the origin might not be stabilizable. At each step, a Lyapunov function is constructed based on a solution of a linear partial differential equation (PDE) or a system of globally asymptotically stable (GAS) ordinary differential equations (ODEs). Optimal and bounded control designs are also addressed. The flexibility of the proposed design is illustrated via five examples.

References

1.
Yu
,
J.
,
Wang
,
J.
,
Zhang
,
C.
, and
Wu
,
Y.
,
2015
, “
Output Feedback Regulation Control for a Class of Uncertain Nonlinear Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
4
), p.
041019
.
2.
Fujioka
,
D.
, and
Singhose
,
W.
,
2018
, “
Optimized Input-Shaped Model Reference Control on Double-Pendulum System
,”
ASME J. Dyn. Syst. Meas. Control
,
140
(
10
), p.
101004
.
3.
Ramirez-Neria
,
M.
,
Sira-Ramirez
,
H.
,
Garrido-Moctezuma
,
R.
, and
Luviano-Juarez
,
R.
,
2016
, “
On the Linear Control of Underactuated Nonlinear Systems Via Tangent Flatness and Active Disturbance Rejection Control: The Case of the Ball and Beam System
,”
ASME J. Dyn. Syst. Meas. Control
,
138
, p.
104501
.
4.
Teel
,
A. R.
,
1992
, “
Feedback Stabilization: Nonlinear Solutions to Inherently Nonlinear Problems
,” Ph.D. thesis, University of California, Berkeley, CA.
5.
Spong
,
M. W.
, and
Praly
,
L.
,
1996
, “
Control of Underactuated Mechanical Systems Using Switching and Saturation
,”
Control Using Logic-Based Switching (Lecture Notes in Control and Information Sciences
),
A.
Stephen Morse
ed., Vol.
222
,
Springer
,
Berlin
, pp.
162
172
.
6.
Do
,
K. D.
, and
Seet
,
G.
,
2010
, “
Motion Control of a Two-Wheeled Mobile Vehicle With an Inverted Pendulum
,”
J. Intell. Rob. Syst.
,
60
(
3–4
), pp.
577
605
.
7.
Castillo
,
P.
,
Dzul
,
A.
, and
Lozano
,
R.
,
2004
, “
Real-Time Stabilization and Tracking of a Four-Rotor Mini Rotorcraft
,”
IEEE Trans. Control Syst. Technol.
,
12
(
4
), pp.
510
516
.
8.
Qian
,
C.
, and
Gong
,
Q.
,
2013
, “
Global Output Feedback Stabilization of a Class of Nonlinear Systems With Multiple Output
,”
ASME J. Dyn. Syst. Meas. Control
,
135
(
4
), p.
044502
.
9.
Teel
,
A. R.
,
1992
, “
Global Stabilization and Restricted Tracking for Multiple Integrators With Bounded Control
,”
Syst. Control Lett.
,
18
(
3
), pp.
165
171
.
10.
Teel
,
A.
,
1996
, “
A Nonlinear Small Gain Theorem for the Analysis of Control Systems With Saturation
,”
IEEE Trans. Autom. Control
,
41
(
9
), pp.
1256
1270
.
11.
Sepulchre
,
R. M.
,
Jankovic
,
V.
, and
Kokotovic
,
P.
,
1997
, “
Integrator Forwarding: A New Recursive Nonlinear Robust Design
,”
Automatica
,
33
(
5
), pp.
979
984
.
12.
Sepulchre
,
R.
,
Jankovic
,
M.
, and
Kokotovic
,
P.
,
1997
,
Constructive Nonlinear Control
,
Springer
,
New York
.
13.
Krstic
,
M.
,
2004
, “
Feedback Linearizability and Explicit Integrator Forwarding Controllers for Classes of Feedforward Systems
,”
IEEE Trans. Autom. Control
,
49
(
10
), pp.
1668
1682
.
14.
Respondek
,
W.
, and
Tall
,
I. A.
,
2008
, “
Feedback Linearizability of Strict Feedforward Systems
,” 47th
IEEE
Conference on Decision and Control, Cancun, Mexico
, Dec. 9–11, pp.
2499
2504
.
15.
Praly
,
L.
,
Ortega
,
R.
, and
Kaliora
,
G.
,
2001
, “
Stabilization of Nonlinear Systems Via Forwarding Via Mod{LgV}
,”
IEEE Trans. Autom. Control
,
46
(
9
), pp.
1461
1466
.
16.
Evans
,
L.
,
2000
,
Partial Differential Equations
,
American Mathematical Society
,
Providence, RI
.
17.
Adomian
,
G.
,
1992
,
Solving Frontier Problems of Physics: The Decomposition Method
,
Kluwer
, Dordrecht, The Netherlands.
18.
Krstic
,
M.
, and
Li
,
Z. H.
,
1998
, “
Inverse Optimal Design of Input-to-State Stabilizing Nonlinear Controllers
,”
IEEE Trans. Autom. Control
,
43
(
3
), pp.
336
350
.
19.
Hardy
,
G.
,
Littlewood
,
J. E.
, and
Polya
,
G.
,
1989
,
Inequalities
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.
20.
Krstic
,
M.
, and
Deng
,
H.
,
1998
,
Stabilization of Nonlinear Uncertain Systems
,
Springer
,
London
.
21.
Sbarbaro
,
D.
,
Tomizuka
,
M.
, and
de la Barra
,
B. L.
,
2009
, “
Repetitive Control System Under Actuator Saturation and Windup Prevention
,”
ASME J. Dyn. Syst. Meas. Control
,
131
(
4
), p.
044505
.
22.
Krstic
,
M.
,
Kanellakopoulos
,
I.
, and
Kokotovic
,
P.
,
1995
,
Nonlinear and Adaptive Control Design
,
Wiley
,
New York
.
23.
Do
,
K. D.
,
2009
, “
Output-Feedback Formation Tracking Control of Unicycle-Type Mobile Robots With Limited Sensing Ranges
,”
Rob. Auton. Syst.
,
57
(
1
), pp.
34
47
.
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