Approximation-free prescribed performance control for unknown SISO pure feedback systems

A universal control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed performance and bounded signals in the closed loop. In this paper, by prescribed performance, it is meant that the output error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value. The proposed approximation-free and low-complexity control scheme isolates the output performance from the control gains selection and exhibits strong robustness against model uncertainties. In fact, any system in pure feedback form obeying certain controllability assumptions can be controlled by the proposed scheme without altering either the controller structure or the control gain values. Finally, a simulation study clarifies and verifies the approach.