A Constructive Approach for Neural Network Approximation Sets in Adaptive Control of Strict-Feedback Systems

Determining the neural network (NN) approximation sets for adaptive control of strict-feedback uncertain systems has posed a persistent challenge. This article proposes a novel and constructive solution that incorporates signal substitution technique, barrier functions (BFs), and backstepping approach. By applying the signal substitution technique, all system states are transformed into state error variables, facilitating the approximation of unknown system functions through NNs. The use of BFs subsequently allows for the restriction of state errors, enabling the calculation of exact bounds for the NN weight estimators. This process reveals the determination of the approximation sets of NN in advance. Illustrative examples are conducted to validate the effectiveness of the proposed approach.