Direct nonlinear order reduction with variational analysis

The variational analysis has been employed in for order reduction of weakly nonlinear systems. For a relatively strong nonlinear system, this method will mostly lose efficiency because of the exponentially increased number of inputs in higher order variational equations caused by the individual reduction process of the variational systems. Moreover, the inexact inputs into the higher order variational equations indispensably introduce extra errors in the order reduction process. Inspired by the variational analysis, we propose a direct model order reduction method. The order of the approximate polynomial system of the original nonlinear system is directly reduced by one project space. The proposed direct reduction technique can easily avoid the errors brought by inexact inputs and the exponentially increased inputs. We show theoretically and experimentally that the proposed method can achieve much more accurate reduced system with smaller order size than the conventional variational equation order reduction method.