Prescribed-time control for a class of semilinear hyperbolic PDE-ODE systems
Résumé
A prediction-based controller is shown to achieve prescribed-time stabilization of a nonlinear infinite-dimensional system, which consists of a general boundary controlled firstorder semilinear hyperbolic PDE that is bidirectionally interconnected with nonlinear ODEs at its unactuated boundary. The approach uses a coordinate transformation to map the nonlinear system into a form suitable for control. In particular, this transformation is based on predictions of system trajectories, which can be obtained by solving a general nonlinear Volterra integrodifferential equation. Then, a prediction-based controller is designed to stabilize the system in prescribed-time. Numerical simulations illustrate the performance of both the prescribed-time controller and an asymptotically stabilizing one, which follows as a special case.
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