Splitting model reduction for bilinear control systems

In this paper, based on low-rank balanced truncation (BT), we present a splitting model reduction method for bilinear control systems with nonzero initial conditions. By analyzing Volterra series, the original bilinear control system is split up into two systems: one is a bilinear control system with zero initial condition, and the other is our constructed control system. Specifically, we prove that the Volterra series containing initial condition of the original system converges to the output of our constructed control system. Thus, we develop a new splitting model reduction method that involves reducing two systems independently by low-rank BT method and then combining the reduced outputs into an aggregate output. A nonlinear RC circuit and a heat transfer model are taken as numerical examples to illustrate the effectiveness of our proposed method.