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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. [ABSTRACT FROM AUTHOR]

With the motivation to provide tools for model-structure selection in LPV identification, in this section modeling of physical systems described by nonlinear differential equations is studied in the LPV framework. It is investigated how such a nonlinear system can be realized or approximated by a LPV system, giving models of the original behavior in terms of LPV representations. First an overview is presented of the available LPV modeling methods. Then, an algorithmic approach is introduced that ensures errorless conversion of nonlinear differential equations into LPV kernel representations. The approach explores adequate choices of the scheduling variable. Based on equivalent sate-space, input-output or orthonormal basis functions based representation of the resulting kernel form, an adequate choice of a model structure can be obtained for the LPV identification of the physical system. [ABSTRACT FROM AUTHOR]

This chapter is devoted to the discretization of LPV systems through the discrete-time projection of their state-space representations. Both exact and approximative approaches are developed in a zero-order hold setting. Primary attention is given to the discretization of state-space representations with static coefficient dependence. For this case, criteria are derived to assist the choice of the sampling-time in terms of preservation of frozen dynamic stability and acceptable upperbound on the discretization error. [ABSTRACT FROM AUTHOR]

In this chapter, series-expansion representations of LPV systems for a given IO partition are developed using the framework of the behavioral approach. In fact, expansion of DT asymptotically stable LPV systems is considered in terms of OBFs and the connection between this type of expansion and the gain-scheduling principle is explored. It is shown that this series-expansion representation is unique and always exists for the considered system class and in some cases only a finite number of the expansion coefficients are nonzero. This implies that finite truncation of a OBFs-based series-expansion can be used as a model structure for the identification of asymptotically stable DT-LPV systems similar to the LTI case. [ABSTRACT FROM AUTHOR]

In this chapter, we continue the discussion of the LPV behavioral framework by establishing equivalence transformations between the state-space and the input-output representation domains. These equivalence transformations enable the comparison and analysis of LPV model structures and provide essential tools to formulate the identification approach of this thesis. First we define LPV canonical forms based on the concept of observability and reachability and we give an algorithmic scheme to construct them from an existing SS representation of the system. Then, transformations are introduced which provide an equivalent IO representation of a SS representation and vice versa. In both cases, the introduced LPV canonical forms are special cases of the transformation problem, serving as a simple gateway between the representation domains. [ABSTRACT FROM AUTHOR]

In this chapter, a behavioral framework of LPV systems is introduced as an extension of the LTI behavioral approach. This is done with the intention to give a unified view on LPV system theory, that enables to approach LPV system identification in a well-founded system theoretic sense. First we define LPV dynamical systems from the behavioral point of view. Then we introduce the algebraic structure in which we formulate kernel, state-space, and input-output representations of LPV systems. We also analyze the properties of LPV systems in terms of state-observability, state-reachability, and dynamic stability. [ABSTRACT FROM AUTHOR]

This chapter is devoted to the introduction of basic concepts that are fundamental for the theory developed in the subsequent chapters. The notion of orthonormal basis functions (OBFs) is introduced with a brief overview of the most important relations and properties. Next, the basic concepts and theory of LTI system identification are reviewed focusing on prediction-error methods. OBFs related parameterizations and the associated identification approaches are also introduced together with the optimality concept of OBF model structures in terms of the Kolmogorov n-width theory. [ABSTRACT FROM AUTHOR]