A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems

A universal, approximation-free state feedback control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed performance and bounded closed loop signals. 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, having maximum overshoot less than a preassigned level. The proposed state feedback controller isolates the aforementioned output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties, while completely avoiding the explosion of complexity issue raised by backstepping-like approaches that are typically employed to the control of pure feedback systems. In this respect, a low complexity design is achieved. Moreover, the controllability assumptions reported in the relevant literature are further relaxed, thus enlarging the class of pure feedback systems that can be considered. Finally, simulation studies clarify and verify the approach.