Prescribed-Time Stabilization of ODEs with Diffusive Actuator Dynamics

We study the finite-time stabilization of an ODE plant having diffusive infinite-dimensional actuator dynamics. We follow a predictor-feedback approach relying on time-varying backstepping, where the actuator utilizes time-dependent gains selected to stabilize the actuator dynamics as well as the plant within a finite time which can be prescribed independently of the system’s initial conditions. As the attenuative actuator dynamics cascade into the ODE, the time-varying feedback gains result in cascading backstepping kernel PDEs. We utilize differential flatness of the kernel PDE as well as the method of successive approximations in order to recover these kernels.