New results in 2D optimal control theory
The infinite horizon LQ optimal control problem for 2-D linear systems described by the Fornasini-Marchesini model is solved. An orthogonality principle for the optimal solution is established and it is shown that the 2-D algebraic Riccati equation is a direct consequence of it. It is also shown that an other approach allows to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Necessary and sufficient conditions for the solvability and the structure of the solution are derived. The necessity of the PBH stabilizability and detectability properties is proved.
scientific article; zbMATH DE number 811686