Event-triggered boundary consensus force control for PDE modeling multi-flexible manipulators with both actuator delay and communication delay

A distributed adaptive consistency controller is designed for PDE modeling multi-flexible manipulators with both actuator delay and communication delay. The input integral is fed back into the controller to avoid the influence of the actuator delay. The adaptive law is designed to observe the ideal signal for the agent without the ideal signal information. The event-triggered method is used in the adaptive law to reduce information transmission pressure and simplify analysis. Based on the integral Krasovskii Lyapunov function and the adaptive law, the designed controller works even with the unknown communication delay between manipulators. A matrix composed of the system and controller parameters is designed, representing the convergence rate of the system, and the optimization function FMINCON is used to optimize the matrix, in order to obtain appropriate controller coefficients. Control goal realization and the stability of the closed-loop system are proven via the Lyapunov direct method. Simulation results verify the effectiveness of the proposed controller.