From Noisy Data to Hierarchical Control: A Model-Order-Reduction Framework

TL;DR

This paper introduces a data-driven framework for creating reduced-order models of unknown linear systems using noisy data, enabling controller design and refinement without system identification.

Contribution

It proposes a novel semidefinite programming approach to construct ROMs, simulation functions, and interface functions directly from noisy data, facilitating hierarchical control.

Findings

Effective controller synthesis on ROMs with refinement to original system.

Quantitative bounds on model mismatch using simulation functions.

Successful case study demonstrating complex specification enforcement.

Abstract

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.