Overlapping decentralized dynamic optimal control

Abstract

An optimal dynamic output feedback controller design approach is proposed for systems which are required to have an overlapping feedback structure. Such a structure may be either imposed due to some design considerations or selected to match the overlapping structure of the given system. The proposed approach first involves transforming the given system into a larger dimensional system. Decentralized optimal controllers are then designed for this expanded system. These controllers are contracted for implementation on the original system in the final phase. It is shown that if the controller designed for the expanded system achieves stability and satisfies the necessary conditions of optimality for the expanded system, then the contracted controller achieves stability and satisfies the necessary conditions of optimality for the original system. Furthermore, the costs for the original and the expanded systems are equal. The details of overlapping controller design for a particular pattern of overlapping are also illustrated and an example design is presented.