From Noisy Data to Hierarchical Control: A Model-Order-Reduction Framework
A new data-driven method creates simplified models for complex systems without needing to know the underlying physics.
A team from KTH Royal Institute of Technology and UC Berkeley has published a paper titled 'From Noisy Data to Hierarchical Control: A Model-Order-Reduction Framework' on arXiv. The research presents a direct data-driven method for constructing Reduced-Order Models (ROMs) of complex, discrete-time linear dynamical systems whose internal dynamics are unknown and affected by process noise. Crucially, the framework does not require a prior step of system identification; instead, it builds a simplified, lower-dimensional representation of the system directly from a single, noise-corrupted stream of input-state data.
The core innovation lies in using the concept of Simulation Functions (SFs) to formally quantify the relationship between the original, complex system and its simplified ROM. The researchers formulate data-dependent conditions, cast as a Semidefinite Program (SDP), that simultaneously solve for the ROM, the SF, and an interface function. This interface is key—it allows a controller designed and synthesized on the easy-to-handle ROM to be accurately refined and implemented on the original, high-order system. A case study in the paper demonstrates that this hierarchical approach enables the enforcement of complex control specifications that go beyond basic stability, such as performance and safety constraints.
This work bridges a significant gap in control theory and practical engineering. Traditionally, creating controllers for large-scale systems (like autonomous vehicle fleets or smart power grids) requires either a perfect, physics-based model—often unavailable—or extensive, clean data for system identification. This new framework accepts the reality of noisy, limited data from a single operational trajectory, providing a rigorous, optimization-based pipeline from data to a verifiable, hierarchical control strategy. It represents a move towards more automated and data-centric control design for complex, real-world engineered systems.
- Builds Reduced-Order Models (ROMs) directly from a single, noisy data trajectory without system identification.
- Formulates the solution as a Semidefinite Program (SDP) to simultaneously find the ROM, a Simulation Function, and a controller interface.
- Enables hierarchical control design on the simple ROM, then refines it for the complex original system to meet advanced specifications.
Why It Matters
Enables robust control design for complex systems like robotics or infrastructure using only imperfect operational data, bypassing the need for perfect models.