Compressed dynamic models ensure realistic system estimations and control
Dynamics Aware Past-Future Information Bottleneck
Information Theory
Summary
Complex systems that change over time can be hard to understand and control. The authors study a way to simplify these systems by keeping only the most important information about their past and future behaviors. They improve existing methods to guarantee that the simplified model still behaves like a real, physical system. This makes the simplified models more useful for tasks like estimating what’s happening now and controlling the system’s future actions. They tested their method using simulations to show it works.
What this means in practice
- •For control engineers: Produce simplified dynamical models that remain physically valid for designing better control systems.
- •For signal processing teams: Generate reliable compressed representations of time series data that maintain dynamical consistency for improved filtering and prediction.
Tested on simulated data.
Authors
Wooyoung Chung, Stas Tiomkin
Abstract
The simplification of complex dynamical systems is essential for efficient estimation and control. A principled approach to this task is through the lens of information-theoretic compression. The Past-Future Information Bottleneck (PF-IB) provides a theoretical framework for compressing linear dynamical systems. However, the standard formulation often lacks structural consistency, yielding representations that are not realizable as dynamical systems. By constraining the objective to a specific manifold of block Hankel matrices, which we prove is a Lie group, we bridge the gap between PF-IB and realization theory. Our approach ensures that the resulting compressed dynamics are realizable, thereby enabling its direct application to estimation and control. We demonstrate our approach in numerical simulations.