Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design

Area of Science:

• Control Engineering
• Nonlinear System Analysis
• Adaptive Control

Background:

• Addressing actuator faults in unknown nonlinear discrete-time systems is critical for reliable operation.
• Strict-feedback systems with unknown nonlinearities present causal challenges in control design.

Purpose of the Study:

• To develop an optimal fault-tolerant control (FTC) strategy for unknown nonlinear discrete-time systems with actuator faults.
• To design an adaptive auxiliary signal to effectively compensate for actuator faults.

Main Methods:

• Utilizing adaptive critic design (ACD) framework combined with reinforcement learning.
• Employing diffeomorphism theory to transform the system and address causality issues.
• Applying action neural networks (ANNs) for function approximation within a backstepping design.
• Leveraging critic neural networks (CNNs) to approximate the cost function.

Main Results:

• An optimal FTC strategy is proposed, guaranteeing system stability.
• The adaptive auxiliary signal successfully offsets the impact of actuator faults.
• The proposed method achieves optimal control performance for the considered systems.

Conclusions:

• The developed FTC strategy effectively handles unknown nonlinearities and actuator faults.
• The integration of ACD and reinforcement learning provides a robust control solution.
• Simulation examples validate the efficacy of the proposed optimal FTC approach.