Optimal identification experiment design for LPV systems using the local approach

Abstract

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LPV system identification for control using the local approach

“…In other words, we will suppose that v(t) is independent of the scheduling variable p and we will also suppose in the sequel that H(z) is known. As shown in, e.g., [16], these assumptions are not required, but they strongly simplify the notations.…”

“…In order to perform a local LPV identification experiment, a number of important choices have to me made: the operating points at which the local LTI identification experiments will be performed as well as the input spectra that will be used in each of these local LTI identification experiments. As shown, e.g., in [16], these choices strongly influence the accuracy of the identified LPV model. Consequently, it is of importance to be able to perform these choices in an optimal way.…”

“…In our recent paper [16], we have determined a procedure to determine these experimental conditions in such a way that we can guarantee an user-defined model accuracy with the least input energy. In [16], the desired model accuracy was expressed in the form of a constraint P −1 θ > R adm where P θ is the covariance matrix of the estimate of θ 0 (i.e. the size of the uncertainty region of this estimate and thus of the identified LPV model) and R adm an arbitrary matrix.…”

“…In the present paper, we also consider the problem of designing the LPV system identification experiment with the least input energy, but the model accuracy constraint will be now ensuring that the uncertainty of the model is small enough to guarantee that the LPV controller designed based on the identified model achieves satisfactory performance with the unknown true LPV system. As it was the case in [16], the optimal LPV identification experiment under this more complex constraint will also only be made up of a limited amount of local LTI identification experiments.…”

“…Using these robustness tools, convex optimization can indeed be used to verify the robustness of a LPV controller designed based on the identified LPV model. These robustness tools can then be integrated in the optimal experiment design procedure of [16] to derive the LPV identification experiment with the least input energy that nevertheless is guaranteed to yield a model with sufficiently small uncertainty to enable robust LPV control.…”