A Conic Optimization Approach to Structured Model Reduction

Two of the most widely used model order reduction techniques are balanced truncation and singular perturbation. The reason for their widespread uptake is that they provide worst case error bounds between the original and reduced order model, and their computational cost is reasonable (scales as a cube of the state dimension). Unfortunately, these methods require a coordinate transformation that destroys the sparsity structure of the state, input, and output matrices. Thus, the network interpretation of the system is lost. In this talk I will present recent work that allows us to reduce the order of the system without destroying the network structure. Furthermore, we provide error bounds, a clustering method for uncovering network structure, and in the best case can cast the reduction problem as a linear program. This is joint work with Aivar Sootla at the University of Oxford.