05/09/2025, 15:00 — 16:00 — Room P3.10, Mathematics Building
Sérgio Rodrigues, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences
Stabilization of linear and semilinear parabolic equations
A crucial task in control applications is the design of a feedback operator allowing us to compute a control input which is able to stabilize a given dynamical system, being able to respond to small perturbations as well. Feedback inputs are given as a function of the state of the system, which is often not fully available in real world applications. Thus, another crucial task is the design of a dynamic Luenberger observer providing us with an estimate for the unknown state, by using the output of sensor measurements; here, the task is to find an operator that injects the output into the dynamics of the observer.
In this talk, we discuss recent developments on the design of such feedback-input and output-injection operators for models given by parabolic-like equations. The focus is put on the design of simple and explicit operators. Both theoretical and numerical aspects are discussed, including a comparison to more classical operators obtained through optimal control tools and involving the solution of Riccati or Hamilton-Jacobi-Bellman equations.
