Estimating Parameter Regions for Structured Parameter Tuning via Reduced Order Subsystem Models
Many large-scale systems are composed of subsystems operated by decentralized controllers, which are fixed in their structure, yet have parameters to tune. Initial tuning or subsequent adjustments dof those parameters ue to varying operating conditions or changes in the network of interconnected systems, while ensuring stability, performance, and security, pose a challenging task due to the overall complexity and size. Subsystems may not be willing or allowed to expose detailed information for safety and privacy reasons. In some cases, a comprehensive system model might not be available for global tuning, or the resulting problem might be computationally infeasible. To enable meaningful global parameter tuning while allowing for data privacy and security, we propose that the subsystems themselves should provide reduced-order models. These models capture the parametric dependency of the subsystem dynamics on the controller parameters. Specifically, we present a method to construct a region in the subsystems’ parameter space in which the deviation of the subsystem and the reduced-order model stays below a specified error bound and in which both systems are stable. A necessary and sufficient condition for such regions is derived using robust control theory. Notably, sufficiency can be expressed in terms of a linear matrix inequality. We demonstrate the approach by considering the temperature control of a large-scale building complex.