The purpose of this chapter is to present the application of the factorization method of linear elliptic boundary value problems to overdetermined problems. The factorization method of boundary value problems is inspired from the computation of the optimal feedback control in linear quadratic optimal control problems. This computation uses the invariant embedding technique of R. Bellman: the initial problem is embedded in a family of similar problems starting from the current time with the current position. This allows to express the optimal control as a linear function of the current state through a gain that is built using the solution of a Riccati equation. The idea of boundary value problem factorization is similar with a spacewise invariant embedding.
|Title of host publication||Modeling, Simulation and Optimization; Tolerance and Optimal Control|
|Editors||Sc Shkelzen Cakaj|
|Place of Publication||Vukovar, Croatia|
|Publication status||Published - 1 Jan 2010|