Optimal experimental design for LPV identification using a local approach

A common approach for dealing with non-linear systems is to describe the system by a model with parameters that vary as a function of the operating point. Consequently, the non-linear system is seen as a combination of local Linear Time-Invariant (LTI) systems, one for each value of the operating point. Such representations are called Linear Parameter-Varying (LPV) models. Due to the importance of this representation for the control of nonlinear systems, numerous algorithms have recently been developed to identify LPV models. However, the optimal design of such identification experiments remains completely unexplored. In this paper, we consider the so-called local approach for the LPV identification. In the local approach, the local linear models, corresponding to a series of fixed operating points, are identified by performing one identification experiment at each of these operating points. The LPV nature of the system is then retrieved by interpolating the value of the parameters at other operating points for example with a polynomial function which is fitted through the parameters identified at the operating points considered. We present an approach to choose optimally the value of the operating-points at which the local identification experiments will be performed. By optimal, we mean that the value of the operating points are optimized in such a way that the LPV model obtained after interpolation has a maximum accuracy.