A polynomial approximation scheme for nonlinear model reduction by moment matching
For engineers and scientists dealing with high-dimensional nonlinear dynamical systems, this work provides a practical numerical approach to model reduction via moment matching, though it is an incremental extension of existing techniques.
The paper presents a numerical method for solving invariance equations in moment matching for nonlinear model reduction, enabling reduced-order models for high-dimensional systems (state dimension ~1000). The method achieves moment matching and recovers steady-state behavior for nonlinear systems driven by linear and nonlinear signal generators.
We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators.