Dual-critic network-based adaptive dynamic programming for vibration control of a flexible two-link manipulator

This paper investigates the trajectory tracking and vibration suppression control problem for a flexible two-link manipulator. To address the nonlinear characteristics and vibration suppression challenges of the system, a novel adaptive dynamic programming control strategy is proposed. First, the assumed modes method is employed to discretely model the FTLM as an ordinary differential equation. Second, considering the limited prior knowledge of the system, a dual-critic network ADP controller is designed for online updates, incorporating a reference network to enhance the approximation of the target cost function and adaptively generate internal reinforcement signals. Third, through continuous evaluation of system feedback, the method effectively approximates model uncertainties using neural networks, thereby minimizing residual vibration and improving trajectory tracking accuracy. Theoretical analysis based on the Lyapunov direct method demonstrates the stability and robustness of the proposed control system. Numerical simulations and experimental validations on the Quanser platform verify the significant performance advantages of the proposed controller. Compared to conventional RL and NN controllers, the proposed dual-critic ADP method achieves a 27.3 % reduction in tracking error standard deviation, a 22.8 % decrease in maximum tracking error, and a 49.1 % reduction in steady-state vibration, demonstrating superior convergence speed and steady-state performance.