Constructing Linear Parameter Varying Models through Adaptation for the Control of a Class of Nonlinear Systems

Abstract

In this paper a novel method is proposed for constructing linear parameter varying (LPV) system models through adaptation. For a class of nonlinear systems, an LPV model is built using its linear part, and its coefficients are considered as time-varying parameters. The variation in time is controlled by an adaptation scheme with the goal of keeping the trajectories of the LPV system close to those of the original nonlinear system. Using the LPV model as a surrogate, a dynamical controller is built by utilizing self-scheduling methods for LPV systems, and it is shown that this controller will indeed stabilize the original nonlinear system.