Optimal decentralized control design with overlapping structure

Abstract

As many industrial systems have a high complexity; large scale systems became the subject of intensive research in systems and control theory. The complexity of the systems leads to severe difficulties that are encountered in the tasks of analyzing the system and designing and implementing appropriate control strategies algorithms. These difficulties arise mainly from dimensionality, uncertainty and information structure constraints. For these reasons the analysis and synthesis tasks cannot be solved economically in a single step as it is possible for similar analysis and design tasks small system. Therefore, it is common procedure in engineering practice to work with mathematical models that are simpler, but less accurate, then the best available model of a given physical process, "since the amount of computation required analyzing and controlling large scale system grows faster than its size. It has been long recognized that it is beneficial to decompose a large scale system into subsystems, and design controller for each subsystem independently on the basis of the local subsystems dynamics and the nature of their interconnections.In this project, we have taken the advantages of overlapping decomposition technique and its application to design an optimal decentralized controller. We started by inclusion/contraction principle that allows us to create an equivalent higher order system then decomposition's theory to subdivide the whole expanded system into subsystems with lower dimensions and treat them independently. To show the efficiency of our algorithms we proposed optimal centralized control design and the decentralized one followed by a comparison