Dynamic Structure Analysis And Application Of Multi-overlapping Interconnected Systems Based On Inclusion Principle

The interconnected structure of complex system often can change with the external or internal environment, which mainly reflect in the connection or disconnection among subsystems and join or disjoin of subsystem. This paper, based on the inclusion principle, solves the problem of the decomposition and decentralized control in the condition of the change of the complex interconnected system structure, and applies to the multi-area interconnected power system and formation of swarm robots. The main content and the innovation point, in the paper, are summarized as:1. The expanding and contracting transformation matrices, permutation matrices and related complementary matrices applied to the pair-wise decomposition and overlapping decentralized control of the systems with a general structure, based on the interconnected system with a complete net type structure, are defined through the description in general topology.2. As to some interconnected systems with general topology, the paper presents deleting and adding methods of pair-wise subsystems, establishes the corresponding deleting and adding matrices, and makes a combination of both to obtain the structural variation matrices which is used to accomplish the pair-with decomposition and overlapping decentralized control of the dynamic systems with general topology.3. Based on the inclusion principle and pair-wise decomposition, the dynamic structural change of a multi-overlapping interconnected system is researched with subsystems join and disjoins in this paper. Through a combination of subsystem adding and deleting matrix, a pair of column and row group structural variation matrices, based on the change in subsystems quantity, is defined to make the information structure between the subsystem to be joined or disjoined and the related subsystems of the original system connect or disconnect dynamically.4. As to the AGC of a multi-area electric power system, this paper considers two kinds of change mentioned, and take the LQ as the AGC. The simulation result demonstrates the stability of the system after structure changing.5. The pair-wise decomposition and decentralized control of the inclusion principle are applied to formation of swarm robots. This paper also considers this change of some robots joining, and uses the decentralized second order consensus algorithm to achieve the formation and maintenance of robots. The simulation demonstrates the mentioned dynamic structure and stable process.