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

Area of Science:

• Control Engineering
• Artificial Intelligence
• System Dynamics

Background:

• Adaptive control of uncertain systems is challenging.
• Neural networks (NNs) are used for approximating system functions.
• Determining NN approximation sets for strict-feedback systems is a key problem.

Purpose of the Study:

• To propose a novel method for determining neural network approximation sets for adaptive control of strict-feedback uncertain systems.
• To ensure state error bounds and calculate exact bounds for NN weight estimators.
• To validate the proposed approach through illustrative examples.

Main Methods:

• Signal substitution technique to transform system states into state error variables.
• Barrier functions (BFs) to restrict state errors and enable bound calculations.
• Backstepping approach combined with NNs for adaptive control.

Main Results:

• Successfully determined the approximation sets of NNs in advance.
• Achieved restricted state errors using barrier functions.
• Calculated exact bounds for NN weight estimators.
• Validated the effectiveness of the proposed method with examples.

Conclusions:

• The proposed method offers a constructive solution for adaptive control of strict-feedback uncertain systems.
• The integration of signal substitution, barrier functions, and NNs provides precise control over state errors and NN approximation sets.
• This approach enhances the design and stability analysis of adaptive control systems.