On some connections between 2D spectral factorizability and the causal optimal control problem

In this paper the 2D causal optimal control problem is stated and deeply investigated. An explicit equation for the optimal input is derived, even if it appears very difficult to deal with. The 2D spectral factorization problem is introduced, too, and its relationships with the solvability of the previous equation are investigated. The main result consists of a technique for finding the optimal input when spectral factorization can be successfully performed.