Optimal Adaptive Control of Uncertain Nonlinear Continuous-Time Systems With Input and State Delays

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Online adaptive control is crucial for systems with unknown dynamics and time delays.
• Actor-critic neural networks offer a powerful framework for complex control problems.
• Ensuring stability and performance in the presence of uncertainties and delays remains a significant challenge.

Purpose of the Study:

• To develop an online optimal adaptive regulation strategy for nonlinear continuous-time systems.
• To address challenges posed by known state and input delays and uncertain system dynamics.
• To ensure the stability and effectiveness of the proposed control approach.

Main Methods:

• Utilizing an actor-critic neural network architecture for online learning and control.
• Deriving temporal difference error (TDE) using integral reinforcement learning, accounting for system delays.
• Implementing a novel identifier to estimate control coefficient matrices for policy refinement.
• Employing Lyapunov analysis to rigorously prove the boundedness of system states and network parameters.

Main Results:

• Successful online optimal adaptive regulation of nonlinear systems with delays and uncertainties.
• Demonstrated effective estimation of control policies via a novel identifier.
• Validated the boundedness of critical system components including state vectors, critic NN weights, and identification errors.
• Simulation results confirm the efficacy of the proposed actor-critic NN-based approach.

Conclusions:

• The proposed actor-critic neural network approach provides an effective solution for online optimal adaptive regulation in complex nonlinear systems.
• Lyapunov analysis confirms the robustness and stability of the control strategy.
• The method demonstrates significant potential for applications requiring adaptive control under uncertainty and time delays.