Compensation of input delay that depends on delayed input

For nonlinear systems, we develop a PDE-based predictor-feedback control design, which compensates actuator dynamics, governed by a transport PDE with outlet boundary-value-dependent propagation velocity. Global asymptotic stability under the predictor-feedback control law is established assuming spatially uniform strictly positive transport velocity. The stability proof is based on a Lyapunov-like argument and employs an infinite-dimensional backstepping transformation that is introduced. The validity of the proposed controller is illustrated applying a predictor-feedback “bang-bang” boundary control law to a PDE model of a production system with a queue. Consistent simulation results are provided that support the theoretical developments.

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