Hierarchical control of linear systems using extended robust approximate simulation

Abstract

This paper develops a hierarchical control structure for linear systems based on extended robust approximate simulation. In numerous real-world scenarios, systems are subject to external disturbances, and there is a restriction on accessibility to all of their states. Furthermore, these systems are modeled using linear dynamics with high state dimensions. Hence, the control synthesis problem for these concrete systems is computationally challenging, and constructing an abstract model with smaller state dimensions to design the controller would be beneficial. Therefore, we introduce the notion of a extended robust approximate simulation function between the concrete system and the abstract model under a new hierarchical control structure. With this respect, a controller is designed for the abstract model and refined for the concrete system by formulating an observer-based robust interface controller based on H∞ while guaranteeing the desired performance for the concrete system. It is worth noting that an Unknown Input Observer (UIO) is employed in the controller, which circumvents the full-state accessibility of the concrete system. The applicability of the presented approach is demonstrated by controlling bus voltages on a smart grid.