This chapter proposes a PID-learning-type adaptive fuzzy controller (PIDAFC) system for chaotic dynamic systems. The proposed PID-AFC system is comprised of a fuzzy controller and a robust controller. The fuzzy controller is designed to mimic an ideal controller, and the robust controller is designed to dispel the effect of the approximation error between the fuzzy controller and the ideal controller. All the control parameters are on-line tuned in the sense of Lyapunov theorem; thus the stability of the system can be guaranteed. Moreover, to relax the requirement for the bound value in the robust control, a bound estimation is investigated to on-line estimate the approximation error introduced by fuzzy controller. The chattering phenomena in the control efforts can be reduced. Finally, a comparison between a conventional adaptive fuzzy controller (AFC) and the proposed PID-AFC is presented. Simulation results verify that the proposed PID-AFC can achieve better tracking performance and faster tracking error convergence than the conventional AFC for chaotic dynamic systems.
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Hsu, CF., Lee, BK., Lee, TT. (2008). A New Training Algorithm of Adaptive Fuzzy Control for Chaotic Dynamic Systems. In: Chan, A.H.S., Ao, SI. (eds) Advances in Industrial Engineering and Operations Research. Lecture Notes in Electrical Engineering, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74905-1_20
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