Model reduction of nonlinear systems: Tangent space approach

In this paper, we propose a novel approach based on the analysis of linear derivative map for the model reduction of nonlinear system with output measurement. With every nonlinear system one can associate a linear derivative map that evolves vectors on the tangent space. We employ the linear derivative map for the construction of observability gramian on the tangent space and then use it for the purpose of reduced order modeling of nonlinear system. Computation methods based on time domain simulation of system dynamics is proposed for the construction of the empirical gramian. Finally, examples demonstrating the application of the proposed method for the model reduction of dynamical systems are provided.