Low-Order Control Design using a Reduced-Order Model with a Stability Constraint on the Full-Order Model

We consider low-order controller design for large-scale linear time-invariant dynamical systems with inputs and outputs. Model order reduction is a popular technique, but controllers designed for reduced-order models may result in unstable closed-loop plants when applied to the full-order system. We introduce a new method to design a fixed-order controller by minimizing the $L_\infty$ norm of a reduced-order closed-loop transfer matrix function subject to stability constraints on the closed-loop systems for both the reduced-order and the full-order models. Since the optimization objective and the constraints are all nonsmooth and nonconvex we use a sequential quadratic programming method based on quasi-Newton updating that is intended for this problem class, available in the open-source software package GRANSO. Using a publicly available test set, the controllers obtained by the new method are compared with those computed by the HIFOO (H-Infinity Fixed-Order Optimization) toolbox applied to a reduced-order model alone, which frequently fail to stabilize the closed-loop system for the associated full-order model.