A Variable Structure MRAC for a Class of MIMO Systems

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.




References:
[1] Chiang-ju, C., King-Chuan, S., A-Chen, W., and Li-Chen, F., (1996),
"A Robust MRAC Using Variable Structure Design for Multi variable
plants," Automatica, 32,no. 6, pp. 833-848.
[2] Hsu, L., Araujo, A.D., and Costa, R.R., (1994), " Analysis and design of
I/O based variable structure adaptive control," IEEE Trans. Automat.
Control, pp. 4-21.
[3] Hsu, L., (1990), " Variable structure model reference adaptive control
using only I/O measurement: General case," IEEE Trans. Automat.
Control, pp. 1238-1243.
[4] Hung, J.Y., Gao, W., Hung, J.C., (1993), " Variable structure control: A
survey," IEEE Trans. On Indust. Elect. , Vol. 40, no. 1, pp. 2-22.
[5] Karami mohammadi A., (2004), "Variable Structure Model Reference
Adaptive Control, for SIMO Systems, " proceedings of ICCAS2004,
August 25-27, Bangkok, Thiland.
[6] Itkis, U., (1976)," control systems of variable structure," John Wiley &
sons Inc., New york.
[7] Narandra, K.S., Annaswamy, A.M., (1989), " Stable Adaptive Systems,"
Prentice-Hall Int. Inc..
[8] Utkin, V.I., (1978), " Sliding modes and their application in variable
structure systems," New york: MIR.
[9] Cunha, J. P. V. S., Hsu, L., Costa, R. R., & Lizarralde, F. (2003).
Outputfeedback model-reference sliding mode control of uncertain
multivariable systems. IEEE Transactions on Automatic Control, 48(12),
2245-2250.
[10] Imai, A. K., Costa, R. R. and Hsu, L., Multivariable MRAC using
Nussbaum gain. In proceedings of 2001 International symposium on
adaptive and intelligent systems and control.