An adaptive sliding mode control design method is proposed for discrete nonlinear systems where explicit knowledge of the system dynamics is not available. Three-layer feedforward neural networks are used as function approximators for the unknown dynamics. The control law is designed based on the outputs of the approximators, and the sliding surface is defined in terms of a stable polynomial of the system outputs. Convergence of the state trajectories into a small sliding sector is proved. The method is applied to the internal combustion (IC) engine idle speed control problem. Simulation and experimental results are provided. [S0022-0434(00)01702-0]

1.
Utkin, V. I., 1992, Sliding Modes in Control and Optimization, Springer.
2.
Kotta
,
U.
,
1989
, “
Comments on the Stability of Discrete-time Sliding Mode Control Systems
,”
IEEE Trans. Autom. Control
,
AC-34
, pp.
1021
1022
.
3.
Furuta
,
K.
,
1990
, “
Sliding Mode Control of Discrete System
,”
Syst. Contr. Lett.
,
14
, pp.
145
152
.
4.
Spurgeon, S. K., 1991, “Sliding Mode Control Design for Uncertain Discrete-time Systems,” Proc. 30th IEEE Conf. on Decision and Control, Brighton, England, pp. 2136–2141.
5.
Sira-Ramirez
,
S.
,
1991
, “
Non-linear Discrete Variable Structure Systems in Quasi-sliding Mode
,”
Int. J. Control
,
54
, pp.
1171
1187
.
6.
Drakunov
,
S. V.
, and
Utkin
,
V. I.
,
1992
, “
Sliding Mode Control in Dynamic Systems
,”
Int. J. Control
,
55
, pp.
1029
1037
.
7.
Kaynak
,
O.
, and
Denker
,
A.
,
1993
, “
Discrete-time Sliding Mode Control in the Presence of System Uncertainty
,”
Int. J. Control
,
57
, pp.
1177
1189
.
8.
Chan
,
C. Y.
,
1997
, “
Discrete Adaptive Sliding-mode Tracking Controller
,”
Automatica
,
33
, pp.
999
1002
.
9.
Furuta
,
K.
,
1993
, “
VSS Type Self-tuning Control
,”
IEEE Trans. Ind. Electron.
,
40
pp.
37
44
.
10.
Bartolini
,
G.
,
Ferrara
,
A.
, and
Utkin
,
V. I.
,
1995
, “
Adaptive Sliding Mode Control in Discrete-Time Systems
,”
Automatica
,
31
, pp.
769
773
.
11.
Chen
,
F. C.
, and
Khalil
,
H. K.
,
1995
, “
Adaptive Controls of a Class of Nonlinear Discrete-time Systems Using Neural Networks
,”
IEEE Trans. Autom. Control
,
AC-40, pp
791
801
.
12.
Spooner, J. T., Ordonez, R, and Passino, K. M., 1997, “Indirect Adaptive Fuzzy Control for a Class of Discrete Time Systems,” Proc. American Control Conference, Albuquerque, NM, June 4–6, pp. 3311–3315.
13.
Spooner J. T., and Passino, K. M., 1997, “Adaptive Prediction Using Fuzzy Systems and Neural Networks,” Proc. American Control Conference, Albuquerque, NM, June 4–6, pp. 1266–1270.
14.
Hornik
,
K.
,
Stinchcombe
,
M.
, and
White
,
H.
,
1989
, “
Multilayer Feedforward Neural Networks are Universal Approximators
,”
Neural Networks
,
2
, pp.
359
366
.
15.
Kjergaard, L., Nielsen, S., Vesterholm, T., and Hendricks, E., 1994, “Advanced Nonlinear Engine Idle Speed Control Systems,” SAE Paper 940974.
16.
Li, X., and Yurkovich, S., 1998, “Sliding Mode Control of Systems with Delayed States and Controls,” Proc. of the 5th International Workshop on VSS, Florida, Dec.
17.
Funahashi
,
K.
,
1989
, “
On the Approximate Realization of Continuous Mappings by Neural Networks
,”
Neural Networks
,
2
, pp.
183
192
.
18.
Hrovat, D., and Sun, J., 1996, “Models and Control Methodologies for IC Engine Idle Speed Control Design,” Proc. 13th IFAC World Congress, pp. 243–248.
19.
Yurkovich S., and Simpson, M., 1997, “Comparative Analysis for Idle Speed Control: A Crank-angle Domain Viewpoint,” Proc. American Control Conference, pp. 278–283.
You do not currently have access to this content.