Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems

Shaocheng Tong ; Changliang Liu ; Yongming Li

International Journal of Applied Mathematics and Computer Science, Tome 20 (2010), p. 637-653 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

Détail

Publié le : 2010-01-01

Zbl 1214.93064

EUDML-ID : urn:eudml:doc:208013

Bibliographie

[000] Boukezzoula, R., Galichet S.and Foulloy L. (2007). Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure, International Journal of Applied Mathematics and Computer Science 17(2): 233-248, DOI: 10.2478/v10006-007-0021-4. | Zbl 1119.93357

[001] Chen, B. and Liu, X.P. (2005). Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes, IEEE Transactions on Fuzzy Systems 13(6): 832-847.

[002] Chen, B.and Liu, X.P. (2007). Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach, Fuzzy Sets and Systems 158(10): 1097-1125. | Zbl 1113.93068

[003] Chen, B.S., Lee C.H. and Chang, Y.C. (1996). $H^∞$ tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach, IEEE Transactions on Fuzzy Systems 4(1): 32-43.

[004] Coddington, E.A. (1989). An Introduction to Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ. | Zbl 0123.27301

[005] Denai, M.A. and Attia S.A. (2002). Fuzzy and neural control of an induction motor, International Journal of Applied Mathematics and Computer Science 12(2): 221-233. | Zbl 1004.93501

[006] Jiang, Z.P., Marels, I.M.Y. and Wang, Y (1996). A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems, Automatica 32(8): 1211-1215. | Zbl 0857.93089

[007] Jiang, Z.P. and Praly L. (1998). Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica 34(7): 825-840. | Zbl 0951.93042

[008] Jiang, Z.P. (1999). A combined backstepping and small-gain approach to adaptive output feedback control, Automatica 35(6): 1131-1139. | Zbl 0932.93045

[009] Kanellakopopoulos, I., Kokotovic, P.V. and Morse, A.S. (1991). Systematic design of adaptive controllers for feedback linearizable systems, IEEE Transactions on Automatic Control 36(11): 1241-1253. | Zbl 0768.93044

[010] Kristic, M., Kanellakopoulos, I. and Kokotovic, P.V. (1992). Adaptive nonlinear control without over parametrization, System Control Letters 19(3): 177-185. | Zbl 0763.93043

[011] Kristic, M., Kanellakopoulos, I.and Kokotovic, P.V. (1995). Nonlinear and Adaptive Control Design, Wiley, New York, NY.

[012] Qi, R.Y. and Brdys M.A.(2009). Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control, International Journal of Applied Mathematics and Computer Science 19(4): 619-630, DOI: 10.2478/v10006-009-0049-8. | Zbl 1300.93100

[013] Qian, C.J. and Lin W. (2002). Output feedback control of a class of nonlinear systems: A non-separation principle paradigm, IEEE Transactions on Automatic Control 47(10): 1710-1715.

[014] Tong, S.C., He, X.L. and Li, Y.M. (2010a). Direct adaptive fuzzy backstepping robust control for single input single output uncertain nonlinear systems with small-gain approach, Information Sciences 180(9): 1738-1758. | Zbl 1282.93163

[015] Tong, S.C., He, X.L. and Li, Y.M. (2010b). Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach, Fuzzy Sets and Systems 161(6): 771-796. | Zbl 1217.93094

[016] Wang, L.X. (1994). Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice-Hall, Englewood Cliffs, NJ.

[017] Wang, M., Chen, B., Liu, X.P. and Shi, P. (2007). Adaptive fuzzy tracking control for a class of perturbed strictfeedback nonlinear time-delay systems, Fuzzy Sets and Systems 159(8): 949-967. | Zbl 1170.93349

[018] Yang, Y.S. and Zhou, C.J. (2005). Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach, Information Sciences 170(2-4): 211-234. | Zbl 1068.93037

[019] Ye, X. D. (2001). Adaptive nonlinear output-feedback control with unknown high-frequency gain sign, IEEE Transactions on Automatic Control 51(3): 504-511.

[020] Zou, A.M. and Hou Z.G. (2008). Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach, IEEE Transactions on Fuzzy Systems 16(4): 886-867.