LPV Modeling Using the Koopman Operator

Linear parameter-varying (LPV) models have been introduced to describe nonlinear (NL) and time-varying (TV) systems and make use of powerful results of linear control theory. LPV systems extend the notion of linear time invariant (LTI) systems, with the difference that the input/output relations change depending on a scheduling parameter. The goal is to efficiently convert a nonlinear model to an LPV representation with minimal complexity and conservativeness and preserving the system properties. A novel approach for modeling nonlinear systems in terms of a quasi-linear representation is based on the Koopman operator theory. Typically, an infinite-dimensional operator is obtained that requires an approximation for practical applications. Based on the resulting model, an LPV description can be obtained using a velocity-based linearization, which is valid at every operating point.