title: Identification of linear parameter varying models
abstract: We consider identification of a certain class of discrete-time nonlinear systems known as linear parameter varying system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dependence of the system coefficients on the parameters is known. We show how this identification problem can be reduced to a linear regression, and provide compact formulae for the corresponding least mean square and recursive least-squares algorithms. We derive conditions on persistency of excitation in terms of the inputs and scheduling parameter trajectories when the functional dependence is of polynomial type. These conditions have a natural polynomial interpolation interpretation, and do not require the scheduling parameter trajectories to vary slowly. This method is illustrated with a simulation example using two different parameter trajectories
keyphrases: identification linear parameter varying models discrete-time nonlinear systems scheduling parameters functional dependence system coefficients linear regression recursive least-squares algorithms scheduling parameter trajectories parameter trajectories polynomial interpolation interpretation least mean square algorithms persistency of excitation conditions time-varying systems