Stabilization of partial differential equations by sequential action control

We present a framework of sequential action control (SAC) for stabilization systems partial differential equations which can be posed as abstract semilinear problems in Hilbert spaces. follow late-lumping approach and show that the explicitly obtained from variational principles using adjoint information. Moreover, we analyze closed-loop system SAC feedback linear problem with quadratic stage costs. apply this theory to prototypical example an unstable heat equation provide numerical results verification demonstration framework.