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A discrete-time time-varying smooth state feedback controller is presented for the set point control of non-holonomic chained systems. The control law drives the system state to zero with an exponential convergent rate without any assumption on the initial state and the sampling rate. Specifically, the discretised model is broken up into two subsystems, and the first control input is explicitly designed such that the second subsystem is transformed into a perturbed linear time-varying system by introducing a novel state transformation, for which classical linear control techniques can be easily adopted to drive the state to the origin. Simulation results are provided to validate the presented approach.
References
-
-
1)
-
Yuan, H., Qu, Z.: `Continuous time-varying pure feedback control for chained nonholonomic systems with exponential convergent rate', Proc. 17th IFAC World Congress, 2008, Seoul, Korea, p. 15203–15208.
-
2)
-
Di Giamberardino, P., Monaco, S., Normand-Cyrot, D.: `Digital control through finite feedback discretizability', Proc. IEEE Conf. on Robotics and Automation, 1996, p. 3141–3146.
-
3)
-
F.U. Rehman ,
M.M. Ahmed
.
Steering control algorithm for a class of wheeled mobile robots.
IET Proc. Control Theory Appl.
,
4 ,
915 -
924
-
4)
-
J. Wang ,
Z. Qu ,
R. Hull ,
J. Martin
.
Cascaded feedback linearization and its application to stabilization of nonholonomic systems.
Syst. Control Lett.
,
4 ,
285 -
295
-
5)
-
A.M. Bloch
.
(2003)
Nonholonomic mechanics and control.
-
6)
-
Y.-P. Tian ,
S. Li
.
Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control.
Automatica
,
7 ,
1139 -
1146
-
7)
-
D. Nešić ,
A. Teel
.
A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models.
IEEE Trans. Autom. Control
,
7 ,
1103 -
1122
-
8)
-
Z. Qu ,
J. Wang ,
C. Plaisted ,
R. Hull
.
Global-stabilizing near-optimal control design for nonholonomic chained systems.
IEEE Trans. Autom. Control
,
9 ,
1440 -
1456
-
9)
-
Walsh, G.C., Bushnell, L.G.: `Stabilization of multiple input chained form control systems', Proc. 32nd IEEE Conf. on Decision and Control, 1993, p. 959–964.
-
10)
-
Z.P. Jiang
.
Robust exponential regulation of nonholonomic systems with uncertainties.
Automatica
,
189 -
209
-
11)
-
I. Hussein ,
A. Bloch
.
Optimal control of underactuated nonholonomic mechanical systems.
IEEE Trans. Autom. Control
,
3 ,
668 -
682
-
12)
-
K. Zhou ,
J.C. Doyle ,
K. Glover
.
(1996)
Robust and optimal control.
-
13)
-
R.P. Agarwal
.
(2000)
Difference equations and inequalities: theory, methods and applications.
-
14)
-
W. Lin ,
C. Byrnes
.
Design of discrete-time nonlinear control systems via smooth feedback.
IEEE Trans. Autom. Control
,
11 ,
2340 -
2346
-
15)
-
Conticelli, F., Palopoli, L.: `Discrete-time multirate stabilization of chained form systems: convergence, robustness, and performance', Proc. IEEE Conf. on Robotics and Automation, 2001, p. 1463–1468.
-
16)
-
Yamada, M., Ohta, S., Morinaka, T., Funahashi, Y.: `Stabilization of nonholonomic systems in chained form based on sampled data control', Proc. IEEE Conf. on Decision and Control, 2002, p. 348–349.
-
17)
-
Y. Hu ,
S.S. Ge ,
C. Su
.
Stabilization of uncertain nonholonomic systems via time-varying sliding mode control.
IEEE Trans. Autom. Control
,
5 ,
757 -
763
-
18)
-
A. Astolfi
.
Discontinuous control of nonholonomic systems.
Syst. Control Lett.
,
37 -
45
-
19)
-
N. Marchand ,
M. Alamir
.
Discontinuous exponential stabilization of chained form systems.
Automatica
,
343 -
348
-
20)
-
I. Kolmanovsky ,
N.H. McClamroch
.
Developments in nonholonomic control problems.
IEEE Control Syst. Mag.
,
6 ,
20 -
36
-
21)
-
R.W. Brockett ,
R.W. Brockett ,
R.S. Millman ,
H.J. Sussman
.
(1983)
Asymptotic stability and feedback stabilization.
-
22)
-
Chelouah, A., Petitot, M.: `Finitely discretizable nonlinear systems: concepts and definitions', Proc. IEEE Conf. on Decision and Control, 1995, p. 19–24.
-
23)
-
A. Bloch ,
S. Drakunov
.
Stabilization and tracking in the nonholonomic integrator via sliding modes.
Syst. Control Lett.
,
91 -
99
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