## Stable adaptive fuzzy control for MIMO nonlinear systems.(English)Zbl 1231.93054

Summary: An indirect adaptive fuzzy control scheme is presented for a class of multi-input and multi-output (MIMO) nonlinear systems whose dynamics are poorly understood. Within this scheme, fuzzy systems are employed to approximate the plant’s unknown dynamics. In order to overcome the controller singularity problem, the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices, a robustifying control term is used to compensate for the lumped errors, and all parameter adaptive laws and robustifying control term are derived based on Lyapunov stability analysis. The proposed scheme guarantees that all the signals in the resulting closed-loop system are uniformly ultimately bounded (UUB). Moreover, the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large. A simulation example is used to demonstrate the effectiveness of the proposed control scheme.

### MSC:

 93C42 Fuzzy control/observation systems 93D15 Stabilization of systems by feedback
Full Text:

### References:

 [1] Wang, L.X., Adaptive fuzzy systems and control- design and stability analysis, (1994), Prentice Hall New Jersey [2] Chen, B.S.; Lee, C.H.; Chang, Y.C., $$H^\infty$$ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE transactions on fuzzy systems, 2, 4, 32-43, (1996) [3] Koo., Keun-Mo, Stable adaptive fuzzy controller with time-varying dead-zone, Fuzzy sets and systems, 121, 161-168, (2001) · Zbl 0993.93019 [4] Tong, S.C.; Li, H.X., Direct adaptive fuzzy output tracking control of nonlinear systems, Fuzzy sets and systems, 128, 1, 107-115, (2002) · Zbl 0995.93512 [5] Chang, Y.C., Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and $$H^\infty$$ approaches, IEEE transactions on fuzzy systems, 9, 2, 278-292, (2001) [6] Mehrdad, H.; Saeed, G., Hybrid adaptive fuzzy identification and control of nonlinear systems, IEEE transactions on fuzzy systems, 10, 2, 198-210, (2002) [7] Chang, Y.C., Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 36, 1535-1545, (2000) · Zbl 0967.93060 [8] Tong, S.C.; Li, H.X., Fuzzy adaptive sliding model control for MIMO nonlinear systems, IEEE transactions on fuzzy systems, 11, 3, 354-360, (2003) [9] Tong, S.C.; Tang, J.; Wang, T., Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets and systems, 111, 2, 153-167, (2000) · Zbl 0976.93049 [10] Boulkrounea, A.; Tadjineb, M.; Saadc, M.M.; Farzac, M., Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction, Fuzzy sets and systems, 161, 6, 797-820, (2010) · Zbl 1217.93086 [11] Labiod, S.; Boucherit, M.S.; Guerra, T.M., Adaptive fuzzy control of a class of MIMO nonlinear systems, Fuzzy sets and systems, 151, 59-77, (2005) · Zbl 1142.93365 [12] Labiod, S.; Guerra, T.M., Direct adaptive fuzzy control for a class of MIMO nonlinear systems, International journal of systems science, 38, 8, 665-675, (2007) · Zbl 1128.93032 [13] Ordonez, R.; Passino, K.M., Stable multi-input multi-output adaptive fuzzy/neural control, IEEE transactions on fuzzy systems, 7, 3, 345-353, (1999) [14] Horn, R.A.; Johnson, C.R., Matrix analysis, (1990), Cambridge University Press · Zbl 0704.15002 [15] Slotine, J.E.; Li, W., Applied nonlinear control, (1991), Prentice-Hall EnglewoodCliffs, NJ · Zbl 0753.93036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.