Feedback control via inertial manifolds for nonautonomous evolution equations (Q652011)

In [Lect. Notes Control Inf. Sci. 154, 22--27 (1991; Zbl 0742.93030)], \textit{P. Brunovský} suggested a method to control the dynamics of evolution equations using finite-dimenstional controllers. The authors of the present paper extend these results to nonautonomous evolution equations. This is based on their earlier results on constructing corresponding inertial manifolds (i.e., finite-dimensional attractive invariant manifolds) using the graph transform rather than the Lyapunov-Perron method. In particular, they obtain inertial manifolds of lower dimension, as illustrated using two examples.