Moment matching model reduction for network systems

The complex network systems consist of multiple dynamical subsystems which are interacting through a complex graph. The order of mathematical models arising from network modeling easily becomes very large. Examples include the electrical circuits, multi-agent systems, and the distributed-parameter systems. Their high order and complexity complicates the analysis and control of such network systems. Therefore, it is worth addressing a structure preserving model reduction problem for network systems. The goal of this research is to find a reduced network system to approximate the behavior of the original network system well. Moment matching methods represent efficient tools in the field of model reduction and have been widely used to solve the structure preserving model reduction problems with different structure constraints. The key idea of the moment matching model reduction method is to equalize a number of the leading coefficients of the Laurent series expansion of the transfer function of the full order system with that of the reduced-order system at selected points in the complex plane. This class of model reduction methods have the advantage of a computationally efficient implementation, which is of big advantage for network systems. However, the limitations are that the stability of the reduced-order system can not be guaranteed, as well as a prior approximation error bound. Therefore, this research aims at extending the moment matching model reduction method to preserve the network structure throughout the approximation. Also, it is desirable to obtain the prior approximation error bound.