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Identification and control of LPV systems using orthonormal basis functions

Project members: P.M.J. Van den Hof, C.W. Scherer, V. Verdult, P.S.C. Heuberger, R.T. Tóth

Sponsored by: NWO

Orthogonal basis functions have a long history in the context of system approximation and identification. Examples are the standard pulse basis and the Laguerre basis. These are both special cases of a more general construction in which the basis functions are generated by a cascaded network of all-pass filters. Typically basis function models are parameterized as


where $\{\phi_k(z)\}$ denotes the set of basis functions and $\{c_k\}$ is the set of coefficients (parameters). An important advantage of this parameterization is that the model parameters appear linearly (this implies that in least squares settings the optimum is unique and easily calculated). Furthermore it leads to an output error structure (consistent estimation of the transfer function, irrespective of noise). This project aims at the exploration of the possible advantages of orthogonal basis functions for the modeling and control of non-linear systems.

Many practical (control) systems involve phenomena that are not only functions of time, but also of other independent variables, such as, e.g., space coordinates. Furthermore, these functions are sometimes nonlinear and/or non-stationary. As a result the accurate modeling of such systems is in general a complex and tedious task, involving the use of nonlinear partial differential equations, leading to models with a huge number of parameters and high computational complexity. On the other hand accurate and efficient control of the relevant process variables is of paramount importance to satisfy the increasing performance demands. In order to achieve these goals, control algorithms and methods have to be applied that require process models of low complexity. This project aims at the development and application of a new generation of tools for identification and control of these processes, enhancing results recently obtained in systems and control theory, with the goal to bridge this obvious gap between modeling and control requirements by the creation of relatively simple models, that are both accurate in the representation of the overall system behavior, suited for control design. One of the approaches taken will consist of interpolation of locally linear models, combining the theory on LPV (linear parameter varying) systems and the theory on orthogonal basis functions.


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