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Stable adaptive fuzzy controller with time-varying dead-zone. (English) Zbl 0993.93019

The study is concerned with the development of an adaptive fuzzy control for a class of dynamic systems of the form \[ x^{(n)}(t)= f({\mathbf x}(t))+ g({\mathbf x}(t)) u(t), \] where the feedback linear control takes on the form \[ u(t)=(-f({\mathbf x})+ v(t))/g({\mathbf x}) \] \((v(t)= x^{(n)}_d(t)- a_n x^{\sim(n-1)}(t)-\cdots- a_1x^{\sim}(t))\) with \(x^\sim(t)\) being the difference between \(x(t)\) and the desired trajectory \(x_d(t))\). It is shown how fuzzy rule-based systems are used to approximate the unknown functions \(f({\mathbf x})\) and \(g({\mathbf x})\) standing in the system’s description. The adaptation laws involve the use of a dead-zone whose size is adaptively adjusted. It is demonstrated that the control law and adaptation scheme guarantee that all signals and parameter estimates remain bounded and the convergence of the tracking error is achieved.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
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References:

[1] Bernard, J. A., Use of rule-based system for process control, IEEE Control Systems Mag., 8, 5, 3-13 (1988)
[2] Buckley, J. J., Sugeno type controllers are universal controllers, Fuzzy Sets and Systems, 53, 299-304 (1993) · Zbl 0785.93057
[3] Castro, J. L., Fuzzy logic controllers are universal approximators, IEEE Trans. Systems Man Cybernet., 25, 4, 629-635 (1995)
[4] Fabri, S.; Kadirkamanathan, V., Dynamic structure neural networks for stable adaptive control on nonlinear systems, IEEE Trans. Neural Networks, 7, 5, 1151-1167 (1996)
[5] Kickert, W. J.M.; Van Nauta Lemke, H. R., Application of a fuzzy controller in a warm water plant, Automatica, 12, 4, 301-308 (1976)
[6] Lee, C. C., Fuzzy logic in control systemsfuzzy logic controller: Part I & II, IEEE Trans. Systems Man Cybernet., SMC-20, 2, 404-435 (1990)
[7] Narendra, K. S.; Annaswamy, A., Stable Adaptive Systems (1989), Prentice-Hall Inc.: Prentice-Hall Inc. Englewood Cliffs · Zbl 0758.93039
[8] Peterson, B. B.; Narendra, K. S., Bounded error adaptive control, IEEE Trans. Automat. Control, AC-27, 1161-1168 (1982) · Zbl 0497.93026
[9] Sanner, R. M.; Slotine, J.-J. E., Gaussian networks for direct adaptive control, IEEE Trans. Neural Networks, 3, 6, 837-863 (1992)
[10] Sastry, S.; Bodson, M., Adaptive ControlStability, Convergence, and Robustness (1989), Prentice-Hall Inc.: Prentice-Hall Inc. Englewood Cliffs
[11] Slotine, J.-J. E.; Li, W., Applied Nonlinear Control (1991), Prentice-Hall Inc.: Prentice-Hall Inc. Englewood Cliffs
[12] Su, C.-Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE Trans. Fuzzy Systems, 2, 4, 285-294 (1994)
[13] Sugeno, M.; Nishida, M., Fuzzy control of model car, Fuzzy Sets and Systems, 16, 103-113 (1985)
[14] Tzirkel-Hancock, E.; Fallside, F., Stable control of nonlinear systems using neural networks, Int. J. Robust Nonlinear Control, 2, 63-86 (1992) · Zbl 0756.93046
[15] Wang, L.-X., Adaptive Fuzzy Systems and ControlDesign and Stability Analysis (1994), Prentice-Hall Inc.: Prentice-Hall Inc. Englewood Cliffs
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