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Configuration Design of Bilinear Networked Systems with Minimum Cost Constraints

This paper addresses the control configuration design problem of bilinear networked systems. The cost values of controlling or measuring the variables of different states are nonnegative and nonuniform among the agents. These state variables are directly actuated or measured by the virtual nodes which are introduced for configuration design. Firstly, we model the design as an optimization problem: the minimum cost minimum control configuration (MCMCC). Next, the necessary condition for the solvability of MCMCC is derived. At the same time, an algorithm is given to provide the optimal solution to MCMCC via issue transformation. This algorithm is based on the Dulmage-Mendelson (DM) decomposition of the system bipartite graph and the directed acyclic graph decomposition of the system graph. Furthermore, we provide a novel dynamic graph to verify the coprime paths. This new dynamic graph can avoid circulation when exist the cycles in the system graph. We prove that this algorithm has polynomial computational complexity. Finally, one example is also provided to illustrate the validity of the algorithm.