Scalable Controller Synthesis for Heterogeneous Interconnected Systems Applicable to an Overlapping Control Framework

A scalable $\mathscr {H}_{\infty }$ controller synthesis is proposed that is tractable for heterogeneous large-scale systems. It is applied to a control approach where a distributed controller is implemented in an overlapping augmented state space. The synthesis is based on an existing modeling approach where the coupling of the subsystems is cast as an interconnection channel. This modeling approach is extended to be applicable for the most general case of heterogeneous systems with different kinds of interconnections. An augmentation of the performance channel is introduced that leaves the system norm unchanged. For the interconnected model, the centralized synthesis conditions of the distributed controllers decompose into small problems of the size of the subsystems. The resulting conditions can be solved in a centralized way with considerably reduced complexity. Furthermore, the decomposition facilitates a distributed solution. For the special case of homogeneous subsystems a decentralized design is possible. Stability and performance results are given for the augmented overlapping controller applied to the physical system. The methods and results are also applicable for non-overlapping distributed systems as a special case of overlap. A numerical example is given which illustrates the modeling and the control performance.