From Noisy Data to Hierarchical Control: A Model-Order-Reduction Framework
This work addresses the challenge of hierarchical control for systems with noisy data, offering a data-driven framework that is incremental in its approach.
The paper tackled the problem of constructing reduced-order models for linear dynamical systems with unknown dynamics and process disturbances using noisy data, enabling controller synthesis that enforces complex specifications beyond stability.
This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on the ROM and its refinement to the original system by an interface function designed using noisy data. To achieve this, the notion of simulation functions (SFs) is employed to establish a formal relation between the original system and its ROM, yielding a quantitative bound on the mismatch between their output trajectories. To construct such relations and interface functions, we rely on data collected from the unknown system. In particular, using noise-corrupted input-state data gathered along a single trajectory of the system, and without identifying the original dynamics, we propose data-dependent conditions, cast as a semidefinite program, for the simultaneous construction of ROMs, SFs, and interface functions. Through a case study, we demonstrate that data-driven controller synthesis on the ROM, combined with controller refinement via the interface function, enables the enforcement of complex specifications beyond stability.