Hierarchical Least Squares Optimal Control of 2-D Systems

An indefinite least squares approach to discrete-time linear quadratic control of two-dimensional systems of Roesser type is presented. Initial and final boundary states are constrained to lie in affine subspaces. By introducing a hierarchical decomposition technique, the problem is converted to a collection of similar smaller size problems. Successive use of the decomposition technique renders computational feasibility on substantially larger coordinate grids than without decomposition. Necessary and sufficient conditions for existence of a unique optimal solution are provided in terms of the smaller size problems.