Model-order reduction is an essential tool for large-scale systems introduced by modern technologies for which full order controller design and implementation may be numerically and computationally infeasible. Model order reduction is a well established field of research in control and systems theory. Of particular interest in recent years is the study of model reduction for multi-agent systems which are characterized by their increasingly large scales.
In this talk, we reexamine the well known orthogonal projection-based reduced-order models (PROMs) and their realizations. A novel product form is derived for the reduction error system of these reduced models, and investigating the error system product form, we then define interface-invariant PROMs, model order reductions with projection-invariant input and output matrices. It is shown that for such PROMs the error product systems are strictly proper. Furthermore, exploiting this structure, an analytic H∞ reduction error bound is obtained and an H∞ bound optimization problem is defined. We then leverage these results for model reduction of large-scale multi-agent systems. We show how graph contractions can be used to obtain structure-preserving PROMs, and present a sub-optimal H∞ graph-based efficient algorithm for model reduction of multi-agent systems. We then demonstrate these results on the classical controlled consensus model.
