A Gramians Based Method for Nonlinearity Quantification of Spatio-Temporal Systems

A gramians based method for quantifying the nonlinearity of the control-affine spatio-temporal systems is proposed in this paper. The empirical gramians are computed from the data collected from a nonlinear model derived by collocation method for spatio-temporal systems. This method compares the empirical gramians of the nonlinear model with that of the linearized model at its steady state operating point. This can result in two measures for the nonlinearity of the system: nonlinearity in the input-state behavior and nonlinearity in the state-output behavior, and it indicates that when it is appropriate to approximate a nonlinear model with a linearization around an operating point.