Optimal boundary control and new Riccati equations for highly damped second-order equations
The problem considered in this paper is governed by a system of the form \(w_{tt}- \Delta w- \Delta w_ t= 0\) in \(Q= \Omega\times (0, \infty)\), \(\Omega\subset \mathbb{R}^ n\). We have the boundary conditions \(w(x, 0)= w_ 0\), \(w_ t(x, 0)= w_ 1\), and \(w= u\) on \(\partial\Omega\times (0, \infty)\). The control is effectuated via the function \(u\) in order to minimize the functional \(J(u)= \int^ \infty_ 0 \int_ \Omega (Rw)^ 2 dx+ \int_{\partial\Omega} u^ 2 dx dt\). The author has carried out a complete study of the associated Riccati equation and corresponding optimal control and state. The problem is formulated in an abstract framework applying to more general problems as well.
scientific article; zbMATH DE number 597508