A Priori Guaranteed Evolution Within the Neural Network Approximation Set and Robustness Expansion via Prescribed Performance Control

A neuroadaptive control scheme for strict feedback systems is designed, which is capable of achieving prescribed performance guarantees for the output error while keeping all closed-loop signals bounded, despite the presence of unknown system nonlinearities and external disturbances. The aforementioned properties are induced without resorting to a special initialization procedure or a tricky control gains selection, but addressing through a constructive methodology the longstanding problem in neural network control of a priori guaranteeing that the system states evolve strictly within the compact region in which the approximation capabilities of neural networks hold. Moreover, it is proven that robustness against external disturbances is significantly expanded, with the only practical constraint being the magnitude of the required control effort. A comparative simulation study clarifies and verifies the approach.