Abstract
This paper presents a problem of observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with input delay and unknown control direction. Compared with the existing research, a novel predefined performance controller is proposed, which relaxes the assumption that the initial error is known. In addition, it is difficult to design the controllers due to input delay and nonaffine properties of the pure-feedback systems, which can be simplified by Pade approximation. Moreover, dynamic surface control and Nussbaum functions are applied to overcome the calculation explosion caused by repeated differentiations and unknown control direction, respectively. Based on the above methods, an adaptive fuzzy predefined performance controller is proposed, and it is proved that all the signals of a closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). The tracking errors converge within a predefined range, while the observer estimation errors converge within a small zero region. Finally, the simulation results demonstrate the effectiveness of the proposed control system.
Highlights
In the past years, the adaptive nonlinear systems based on the backstepping method has matured increasingly and received widespread attention in [1, 2]
Complexity mentioning that an adaptive predictor incorporated with a high-order neural network observer was proposed to obtain the predictions of the future system states in pure-feedback systems in [28], which were applied in the control design to avoid the input delay and nonlinearities
An observer-based adaptive fuzzy predefined performance controller has been introduced of a class of nonlinear pure-feedback systems with unknown control direction and input delay
Summary
The adaptive nonlinear systems based on the backstepping method has matured increasingly and received widespread attention in [1, 2]. Complexity mentioning that an adaptive predictor incorporated with a high-order neural network observer was proposed to obtain the predictions of the future system states in pure-feedback systems in [28], which were applied in the control design to avoid the input delay and nonlinearities. The existing predefined performance control methods are insufficient to deal with a class of nonlinear pure-feedback systems with input delay. Based on the above discussion, this article presents a method for observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with unknown control direction and input delay. For a matrix Q, λmin(Q) stands for the smallest eigenvalue of Q and λmax(Q) stands for the largest eigenvalue of Q
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