EAAI Journal 2025 Journal Article
Adaptive neural network tracking control for unknown high-order nonlinear systems: A constructive approximation set based approach
- Yu-Fa Liu
- Yong-Hua Liu
- Jin-Wa Wu
- Jie Tao
- Ming Lin
- Chun-Yi Su
- Renquan Lu
This article addresses the problem of adaptive neural network (NN) tracking control for unknown high-order nonlinear systems, with a focus on accurately constructing NN approximation sets. To guarantee the local approximation capabilities of NNs, it is crucial that their input signals remain within corresponding compact sets. However, the unknown functions and powers in high-order nonlinear systems make it difficult to determine these sets accurately. To solve this, we introduce a novel adaptive NN tracking control strategy that integrates signal substitution technique, barrier functions (BFs), and NNs. Specifically, the signal substitution technique converts the original system states into state error variables, along with the desired reference signal and its time derivatives, which serve as part of the NN input. BFs are employed to constrain the state errors, while NNs approximate the transformed unknown system functions. This approach enables precise calculation of bounds for the NN weight estimators, ensuring that the NN approximation sets are constructed. Unlike existing methods, our approach not only proves the existence of NN approximation sets but also provides a constructive design strategy, significantly enhancing the approximation accuracy for unknown nonlinear functions. Simulation results demonstrate the effectiveness and advantages of the proposed method.