Enhanced state-constrained adaptive fuzzy exact tracking control for nonlinear strict-feedback systems

An adaptive fuzzy exact tracking control (ETC) is constructed of nonlinear strict-feedback systems with full-state constraints, mismatched external disturbances. Compared with barrier Lyapunov function based on exponential-type constraint, a novel arctan-type constraint is proposed for the first time, whose convergence boundary is consistent with the exponential-type constraint and the initial value has a wider range of applicability under the same parameters. Different from dynamic surface control method and command filter method to solve the “differential explosion” in the backstepping design, the differential of the virtual controller is formulated within a polynomial expression, and an estimation of its maximum value is determined. Subsequently, using this upper bound estimation information, an adaptive fuzzy ETC mechanism is constructed. Utilizing this approach, whenever the tracking error diverges from the origin, an associated control mechanism springs into action, guiding it to converge towards and slide along the origin, thereby ensuring exact tracking control. To demonstrate the salient features of this control mechanism, a nonlinear system and a single-link robotic system are employed in simulation studies.