Model Reduction of Nonlinear Differential-Algebraic Equations

A novel approach to balanced truncation of nonlinear systems

“…Recent research has extended this method to also cover the nonlinear case, see [4], its discrete-time counterpart in [5] and for differential-algebraic systems in [6]. Here, a balancing nonlinear coordinate-change is applied followed by truncation of states.…”

Steady-State Matching and Model Reduction for Systems of Differential–Algebraic Equations

“…Remark 8: To obtain the family of reduced order models (18) we only need to solve equation (4). In general the solution of this partial differential-algebraic equation is difficult to determine analytically.…”

“…We consider the model studied in [4], which represents the electrical circuit illustrated in Fig. 1.…”

“…Conversely, only a few methods to reduce nonlinear singular systems have been proposed. A method based on balanced truncation has been proposed in [4]. Further results have been obtained using piecewise-linear model reduction, see [20]- [22].…”

“…multi-body systems, electrical networks, chemical processes, social economic systems [1], and to model large interconnected systems, e.g. systems obtained from the application of the Kirchoff's laws or models created by objectoriented modeling languages such as MODELICA [4], [5].…”