LPV Identification via OBFs

Abstract

All the theory that has been introduced so far has served the sole purpose of providing tools to formulate identification of general LPV systems in a wellestablished manner. Building on the developed tools, a widely applicable identification approach is proposed in this chapter by using model structures that originate from truncated OBF expansion representations of LPV systems. First, under the assumption of static dependence of the expansion coefficients, two identification methods, a local and global one, are developed for the introduced model structures. While the local approach uses the gain-scheduling principle: identification with constant scheduling signals and interpolation of the resulting LTI models, the global approach provides a direct LPV model estimate via linear regression based on data records with varying scheduling trajectories. The approaches are analyzed in terms of variance, bias, consistency, and applicability together with the validation of the model estimates. Finally, to enable the estimation of modes with dynamic coefficient dependencies, a modified feedback-based OBF model structure is proposed and estimation in this framework is formulated through a separable least-squares strategy.