Nussbaum-Based Adaptive Neural Networks Tracking Control for Nonlinear PDE-ODE Systems Subject to Deception Attacks

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Artificial Intelligence

Background:

• Nonlinear partial differential equation-ordinary differential equation (PDE-ODE) coupled systems present unique control challenges.
• Deception attacks on sensors and actuators compromise state/output availability in these systems.
• Existing control methods struggle with the infinite-dimensional nature of PDEs and system coupling under attacks.

Purpose of the Study:

• To develop a novel adaptive neural networks (NNs) tracking control scheme for nonlinear PDE-ODE coupled systems.
• To address the challenges posed by deception attacks that render system states and outputs unavailable.
• To ensure robust tracking performance and signal boundedness despite adversarial conditions.

Main Methods:

• A new coordinate transformation based on the backstepping method is employed to reformulate the PDE subsystem.
• Adaptive neural networks (NNs) are utilized to handle unknown control gains and nonlinearities.
• Nussbaum technology is incorporated to mitigate the effects of uncertainties introduced by attacks.

Main Results:

• The proposed control scheme guarantees that all signals within the coupled PDE-ODE system remain bounded.
• Effective tracking control performance is achieved even when sensors and actuators are under deception attacks.
• Simulation results validate the efficacy of the developed adaptive control strategy.

Conclusions:

• The novel adaptive NNs tracking control scheme is effective for nonlinear PDE-ODE coupled systems facing deception attacks.
• The integration of backstepping, NNs, and Nussbaum technology provides a robust solution.
• The method ensures system stability and reliable performance under sensor and actuator attacks.