Nonlinear Model Reduction in the Loewner Framework
Joel D. Simard, Alessandro Astolfi
Abstract
We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense.
Topics & Concepts
Nonlinear systemMathematicsReduction (mathematics)Interpolation (computer graphics)State spaceLTI system theoryApplied mathematicsInvariant (physics)Mathematical optimizationAlgorithmLinear systemComputer scienceMathematical analysisArtificial intelligenceGeometryPhysicsMathematical physicsMotion (physics)StatisticsQuantum mechanicsModel Reduction and Neural NetworksHydraulic and Pneumatic SystemsReal-time simulation and control systems