Speaker
Description
Linear quadratic Gaussian (LQG) balanced truncation is a model reduction technique for possibly unstable linear time-invariant systems which are to be controlled by an LQG controller. In contrast to the classical balanced truncation approach, the LQG balancing procedure is based on the closed-loop system behavior rather than on the transfer function of the open-loop system. Furthermore, LQG balanced truncation comes with an a priori error bound in the gap metric and yields both a reduced-order model (ROM) for the plant and a corresponding reduced-order controller.
In this talk, we consider the special case where the plant is described by a linear port-Hamiltonian (pH) descriptor system. The pH structure implies many desirable properties such as passivity, which motivates preserving this structure during model reduction. We demonstrate how LQG balanced truncation can be modified such that the ROM is also pH and that this modification still allows for an a priori error bound in the gap metric. Furthermore, we introduce a theoretical approach for exploiting the non-uniqueness of the pH representation to achieve a faster decay of the error bound. This approach is based on a maximal solution of a Kalman-Yakubovich-Popov linear matrix inequality for descriptor systems. Finally, the theoretical findings are illustrated by means of a numerical example.
