Nonlinear system identification using compressed sensing

This paper describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. The differential equations describing the system dynamics are to be determined from measurements of the system´s input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system´s outputs into a sparse superposition of corresponding time-series signals produced by the library components.