Model Reduction of Complex Dynamical Systems: A Sensitivity Based Approach

For model reduction of non-linear state space models the empirical Gramian framework is frequently used in various disciplines (e.g., chemical and mechanical engineering). Numerical computation of empirical Gramians is known to be computationally demanding and not always very accurate. To remedy these inaccuracies, perturbations from steady states are often used, thereby omitting essential dynamics. By analysing the non-linear model reduction problem from a system identification perspective where the initial conditions x(0) are viewed as parameters, we show that these issues are better handled. In addition, our approach allows for an accurate null-space computation of the well-known observability matrix for non-linear systems. These (lack of) observability results can be verified by solving a well-posed problem (in terms of complexity) with computer algebra software. We demonstrate both reduction and observability of a non-linear dynamical system in a few examples.