Distributed proper orthogonal decomposition for large-scale networked nonlinear systems with approximation error bound

Recently, dynamical systems in engineering and science problems become drastically larger and too complex. One of the ways to solve the difficulty is to model a system with a hierarchical network structure. Proper orthogonal decomposition (POD) is a model reduction method using available data. The author of this paper and their colleagues derived a distributed version of the POD (distributed POD) for a large-scale networked linear dynamical system, which can specify the degree of approximation of subsystems and preserve the network structure. The ℓ₁-norm minimizing POD was also proposed for a construction of a simple network structure. In this paper, we generalize both PODs to the nonlinear case as a main result. We also characterize an upper bound of the approximation error of the entire system. A numerical example is provided to show an efficiency of the PODs.