Adaptive Fuzzy Control for State Constrained Pure-Feedback Nonlinear Systems with Input Nonlinearity

This paper focuses on the problem of adaptive fuzzy backstepping control for a class of pure-feedback nonlinear systems with time-varying state constraints, input saturation and dead-zone, and unmatched external disturbances. The adaptive fuzzy models are employed to online approximate some uncertain smooth functions. Unlike many neighboring works, this paper carefully solves the open problem of the feasibility of the virtual control laws in the barrier Lyapunov function-based control design framework. By using disturbance observers in a backstepping framework, the estimation errors due to the use of a priori bounded virtual control law are appropriately compensated and the “explosion of complexity” is practically avoided. The proposed controller ensures the convergence of the output tracking error to an arbitrarily tiny neighborhood of the origin, boundedness of all closed-loop signals and no-violation of the predefined state constraints. A numerical example is provided to validate the effectiveness of the proposed method.