Nonlinear Predictor Feedback Design for State-Dependent Input Delay Integro-Differential Equations

In nonlinear ODE-PDE coupled systems, where propagation speed depends on the integral of ODE states over a specified past period, we develop a trilayer predictor-feedback control strategy to fully compensate for input delays associated with the double integral of the ODE states. Assuming bounded transport velocity, we establish global asymptotic stability of the closed-loop system in the infinity norm through a predictor-based backstepping transformation. We model a buffer driven production system and perform numerical experiments to demonstrate the effectiveness of our control approach using a previously introduced piecewise exponential bang bang control law as the nominal (delay-free) feedback design.