Overlapping state-input-output decomposition of complex systems with guaranteed structural observability and controllability.

Decomposing a complex dynamic system into lower-order subsystems is a valuable strategy in various fields as it overcomes the challenges posed by system complexity. In this paper, an overlapping ϵ-decomposition with guaranteed structural observability and controllability is proposed for complex dynamic systems. The proposed decomposition approach relies on optimization and graph theory. To accomplish this, first, a single optimization problem is formulated to decompose a dynamic system into subsystems with weak coupling that can have overlapping components. Then, the resulting decomposition is extended to ensure the subsystems' structural observability and controllability. A key feature of the presented optimization-based decompositions is their ability to detect both disjoint and overlapping structures of dynamic systems simultaneously and systematically. At last, the effectiveness of the suggested approaches is assessed through simulations conducted on three case studies including a ship boiler, an IEEE 57-bus power system, and an IEEE 300-bus power system.