This study combines self-organizing fuzzy logic control technology with optimal control theory and presents a self-organizing fuzzy optimal controller for under-actuated systems. Instead of calibrating the control input directly, the self-organizing fuzzy optimal controller employs the self-organizing fuzzy system as a superior regulator to adjust the weighting matrix of the cost function for the optimal controller. Through this operation and the hierarchical control architecture design, self-organizing fuzzy optimal controller adaptively regulates the control strategy and manipulates the optimal control procedure according to the system dynamic behavior in real time. The optimal control law corresponding to the proposed regulator is then derived from the maximum principle for optimal control theory. The stability of the self-organizing fuzzy optimal controller is analyzed and proved through the Lyapunov stability theorem. Simulations on an under-actuated gantry crane system and a ball-and-beam system have verified that the self-organizing fuzzy optimal controller provides superior control performances as compared with the traditional linear quadratic regulating controller.
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