Section: New Results

Finite-time/Fixed-time control of PDEs

Participant : Andrey Polyakov.

The paper [40] deals with continuous boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. IT was shown that the time of convergence can be prescribed and is independent of the initial condition of the system. The design of time-varying feedbacks was carried out by using the backstepping approach for which suitable characterizations for time-varying kernels were derived. The work [39] considered the problem of local finite-time stabilization of the viscous Burgers equation. A boundary switched linear control with state dependent switching law was designed based on the backstepping approach. The strategy builds on discontinuous kernels, which render the control function to be piecewise continuous. It was proven that such a control stabilizes locally the viscous Burgers equation and that the settling time depends on initial conditions.