Structured model reduction for dynamical networked systems

Mathematical models of networked systems usually take the form of large-scale, nonlinear differential equations. Model reduction is a commonly used technique for understanding and analyzing systems of this size, by producing simplified yet accurate descriptions for them. Most available reduction methods work well for linear system descriptions or small-scale nonlinear system descriptions but they usually involve a state transformation to ‘balance’ the system before truncation. However, linear or nonlinear state combinations destroy the system structure that is important for drawing conclusions about the original networked system from the reduction. In this paper we propose an algorithmic methodology for model order reduction of nonlinear systems, without inducing state transformations. A priority list of states to be collapsed according to the estimated worst-case 2-norm of the error between the outputs of the original and reduced systems is produced. The main advantage of the method is that the states of the reduced system are a subset of the states of the original system.