×

Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and \(H^{\infty}\) approaches. (English) Zbl 1053.93024

Summary: Fuzzy control is a model-free approach, i.e., it does not require a mathematical model of the system under control. An observer-based indirect adaptive fuzzy neural tracking control equipped with VSS and \(H^{\infty}\) control algorithms is developed for nonlinear SISO systems involving plant uncertainties and external disturbances. Three important control methods, i.e., adaptive fuzzy neural control scheme, VSS control design and \(H^{\infty}\) tracking theory, are combined to solve the robust nonlinear output tracking problem. A modified algebraic Riccati-like equation must be solved to compensate the effect of the approximation error via the adaptive fuzzy neural system on the \(H^{\infty}\) control. The overall adaptive scheme guarantees the stability of the resulting closed-loop system in the sense that all the states and signals are uniformly bounded and arbitrary small attenuation level of the external disturbance on the tracking error can be achieved. The simulation results confirm the validity and performance of the advocated design methodology.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
93B36 \(H^\infty\)-control
Full Text: DOI

References:

[1] Cao, S. G.; Rees, N. W.; Feng, G., Analysis and design of fuzzy control systems using dynamic fuzzy-state space models, IEEE Trans. Fuzzy Systems, 7, 192-199 (1999)
[2] Castro, J. L., Fuzzy logical controllers are universal approximators, IEEE Trans. Systems Man Cybernet., 25, 629-635 (1995)
[3] Chen, B. S.; Lee, C. H.; Chang, Y. C., \(H^∞\) tracking design of uncertain nonlinear SISO systemsadaptive fuzzy approach, IEEE Trans. Fuzzy Systems, 4, 32-43 (1996)
[4] Wang, C.-H.; Liu, H.-L.; Lin, T.-C., Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems, IEEE Trans. Fuzzy Systems, 10, 39-49 (2002)
[5] Cuesta, F.; Gordillo, F.; Aracil, J.; Ollero, A., Stability analysis of nonlinear multivariable Takagi-Sugeno fuzzy control systems, IEEE Trans. Fuzzy Systems, 7, 508-519 (1999)
[6] Hung, J. Y.; Gao, W.; Hung, J. C., Variable structure controla survey, IEEE, Trans. Indust. Electron., 40, 2-22 (1993)
[7] Khalil, H. K., Adaptive output feedback control of nonlinear systems represented by input-output models, IEEE Trans. Automat. Control, 41, 177-188 (1996) · Zbl 0842.93033
[8] Leu, Y. G.; Lee, T. T.; Wang, W. Y., Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems, IEEE Trans. Systems Man Cybernet., 29, 583-591 (1999)
[9] Leu, Y. G.; Lee, T. T.; Wang, W. Y., Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems, IEEE Trans. Robotics Automat., 15, 805-817 (1999)
[10] Ma, X. J.; Sun, Z. Q., Output tracking and regulation of nonlinear system based on Takgi-Sugeno fuzzy model, IEEE Trans. Systems Man Cybernet., 30, 47-59 (2000)
[11] Marcelo, C. M.; S. H. Zak, Teixeira., Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE Trans. Fuzzy Systems, 7, 133-142 (1999)
[12] Marino, R.; Tomei, P., Globally adaptive output-feedback control on nonlinear systems, Part Ilinear parameterization, IEEE Trans. Automat. Control, 38, 17-32 (1993) · Zbl 0783.93032
[13] Marino, R.; Tomei, P., Globally adaptive output-feedback control on nonlinear systems, Part IInonlinear parameterization, IEEE Trans. Automat. Control, 38, 33-48 (1993) · Zbl 0799.93023
[14] Narendra, K. S.; Parthasarathy, K., Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Networks, 1, 4-27 (1990)
[15] Park, A. S.; Yu, W.; Sanchez, E. N.; Perez, J. P., Nonlinear adaptive tracking using dynamic neural networks, IEEE Trans. Neural Networks, 10, 1402-1411 (1999)
[16] Rovithakis, G. A.; Christodoulou, M. A., Adaptive control of unknown plants using dynamical neural networks, IEEE Trans. Systems Man Cybernet., 24, 400-412 (1994) · Zbl 1371.93112
[17] Rovithakis, G. A.; Christodoulou, M. A., Direct adaptive regulation of unknown nonlinear dynamical systems via dynamic neural networks, IEEE Trans. Systems Man Cybernet., 25, 1578-1594 (1995)
[18] Sastry, S.; Bodson, M., Adaptive Control Stability, Convergence, and Robustness (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0721.93046
[19] Sastry, S. S.; Isidori, A., Adaptive control of linearization systems, IEEE Trans. Automat. Control, 34, 1123-1131 (1989) · Zbl 0693.93046
[20] Slotine, J. E.; Li, W., Applied Nonlinear Control (1991), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0753.93036
[21] Spooner, J. T.; Passino, K. M., Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Systems, 4, 339-359 (1996)
[22] Sugeno, M., On stability of fuzzy systems expressed by fuzzy rules with singleton consequents, IEEE Trans. Fuzzy Systems, 7, 201-224 (1999)
[23] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Systems Man Cybernet., 15, 116-132 (1985) · Zbl 0576.93021
[24] Wang, L. X., Stable adaptive fuzzy control of nonlinear systems, IEEE Trans. Fuzzy Systems, 1, 146-155 (1993)
[25] Wang, L. X., Adaptive Fuzzy Systems and Control: Design and Stability Analysis (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[26] Wang, C. H.; Wang, W. Y.; Lee, T. T.; Tseng, P. S., Fuzzy B-spline membership function (BMF) and its applications in fuzzy-neural control, IEEE Trans. Systems Man Cybernet., 25, 841-851 (1995)
[27] Chang, Yeong-Chan, Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and
((H^{..}\) approaches, IEEE Trans. Fuzzy Systems, 9, 278-292 (2001)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.