Optimization based LPV-approximation of multi-model systems

Abstract

In this paper we have formulated the problem of finding an LPV-approximation to a system as an optimization problem. For this optimization problem we have presented two possible ways to solve this. The problem is posed as a model reduction problem and formulated such that it should try to preserve the input-output behavior of the system. In the two examples in the paper the potential of the new methods are shown. We have also shown the benefits of using model reduction techniques to capture the input-output behavior to obtain accurate low order LPV-approximations. One method uses SDP-optimization to solve the problem. SDP-optimization has been a hot topic during the last years, but the problem with the SDP method is that it scales badly with the dimension of the problem. Also here it has bilinear constraints which makes the problem really difficult. With the other method we try to use a more general nonlinear approach which seem to be more suitable for this problem. For this method we have also calculated a gradient that can be used to apply a descent or Newton-like method to solve the problem.

Robust generation of LPV state-space models using a regularized &#x210C;<inf>2</inf>-cost

“…In this paper we extend the idea presented in [8], by adding a problem-specific regularization to the problem. We give a robust optimization interpretation of the regularization and motivate it with some examples.…”

An H∞-norm-based approach for operating point selection and LPV model identification from local experiments

“…In order to address this coherent basis issue, a new approach, sharing ideas from D. Petersson's work [21], is suggested hereafter. As explained first in [22,23], then in [36,35], the standard interpolation step involved in the local approach can be efficiently discarded by optimizing one global cost-function which fits the local behavior of the sought global LPV model (with coherent local and global state basis) to the available local information available in the local LTI models estimated during the second step of the local approach. However, contrary to the developments available in [21,24], we do not consider an H 2 -normbased optimization solution hereafter but an H ∞ -norm-based one.…”

LPV system identification using series expansion models

“…This means that the final LFR form of the identified model (37) is relatively large with dim(x) = 4 + 2 · 16 = 36 and dim(z) = 2 · 17 = 34. However, by applying recent methods in LPV model reduction, like the approach of [Petersson and Löfberg (2009)], this LFR form can be reduced to state dimension 8 and with dim(z) = 5, without a significant loss of accuracy. The explanation lays in the fact that in the considered model structure Eq.…”