Adaptive Fuzzy Control of Nonlinear Systems in Pure Feedback Form Based on Input-to-State Stability

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Using mean value theorem and backstepping technique, a robust adaptive fuzzy control scheme is proposed for a class of pure-feedback nonlinear systems with unknown dead zone and disturbances via input-to-state stability. Takagi–Sugeno (T--S) type fuzzy logic systems are used to approximate the uncertain nonlinear functions and fewer learning parameters need to be adjusted online. Based on small gain theorem, the closed-loop control system is proven to be semiglobally uniformly ultimately bounded, and the tracking error converges to a neighborhood of zero by choosing appropriate parameters. Simulation results demonstrate the effectiveness of the control scheme. </para>