Summary An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.

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This paper studies the full-state and input constraints of uncertain nonlinear pure-feedback systems. The radical constraint functions are proposed, which avoids the drawbacks of the barrier Lyapunov functions and the logarithmic constraint functions. At the same time, a control algorithm based on fuzzy control is proposed to avoid the "explosion of terms" problem of the backstepping method. In addition, this paper avoids an Assumption of nonaffine function, which reduces the conservatism and increases the applicability of the algorithm. This control algorithm is proposed so that all signals of the closed-loop system are the semi-globally uniformly ultimately bounded, and the tracking error converge to a small neighborhood of the origin, and all states and input of nonlinear pure-feedback systems can be constrained. Finally, simulation results are provided to verify the effectiveness of the proposed approach.