Optimization based LPV-approximation of multi-model systems

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.