Robust tracking control for nonlinear MIMO systems via fuzzy approaches. (English) Zbl 0967.93060

A former approach of B.-S. Chen, T.-C. Lee and Y.-C. Chang [IEEE Trans. Fuzzy Systems 4, 32-43 (1996)] towards the treatment of nonlinear control problems by fuzzy control techniques is here extended to the multidimensional case. Starting from a system of differential equations which include some smooth nonlinearities in some coefficients, an approximating fuzzy control system is constructed. For it, sufficient conditions are given under which the fuzzy control strategy works in such a way that the tracking error remains within prescribed bounds.


93C42 Fuzzy control/observation systems
93C35 Multivariable systems, multidimensional control systems
93C10 Nonlinear systems in control theory
Full Text: DOI


[1] Başar, T.; Berhard, P., \(H^∞\)-optimal control and related minimax problems (1990), Birkhäuser: Birkhäuser Germany, Berlin
[2] Chang, Y. C.; Chen, B. S., A nonlinear adaptive \(H^∞\) tracking control design in robotic systems via neural networks, IEEE Transactions on Control Systems Technology, 5, 13-29 (1997)
[3] Chen, B. S.; Lee, C. H.; Chang, Y. C., \(H^∞\) tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach, IEEE Transactions on Fuzzy Systems, 4, 32-43 (1996)
[4] Horn, R. A.; Johnson, C. R., Matrix analysis (1985), Cambridge University Press: Cambridge University Press New York · Zbl 0576.15001
[5] Ioannou, P. A.; Sun, J., Robust adaptive control (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0839.93002
[6] Jankovic, M., Adaptive nonlinear output feedback tracking with a partial high-gain observer and backstepping, IEEE Transactions on Automatic Control, 42, 106-113 (1997) · Zbl 0872.93043
[7] Johansen, T. A.; Ioannou, P. A., Robust adaptive control of minimum phase nonlinear systems, International Journal of Adaptive Control and Signal Processing, 10, 61-78 (1996) · Zbl 0849.93037
[8] Karsenti, L.; Lamnabhi-Lagarrigue, F.; Bastin, G., Adaptive control of nonlinear systems with nonlinear parameterization, Systems and Control Letters, 27, 87-97 (1996) · Zbl 0875.93230
[9] Khalil, H. K., Adaptive output feedback control of nonlinear systems represented by input-output models, IEEE Transactions on Automatic Control, 41, 177-188 (1996) · Zbl 0842.93033
[10] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V., Nonlinear and adaptive control design (1995), Wiley: Wiley New York · Zbl 0763.93043
[11] Marino, R.; Tomei, P., Global adaptive output-feedback control of nonlinear systems, Part I: linear parameterization and Part II: nonlinear parameterization, IEEE Transactions on Automatic Control, 38, 17-49 (1993) · Zbl 0783.93032
[12] Spooner, J. T.; Passino, K. M., Stable adaptive control using fuzzy systems and neural networks, IEEE Transactions on Fuzzy Systems, 4, 339-359 (1996)
[13] Su, C. Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE Transactions on Fuzzy Systems, 2, 285-294 (1994)
[14] Wang, L. X., Adaptive fuzzy systems and control: design and stability analysis (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
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