Data-Driven Nonconvex Reachability Analysis using Exact Set Propagation
A new mathematical framework enables exact, nonconvex reachability analysis for AI systems with unknown dynamics.
A team from KTH Royal Institute of Technology and TU Berlin has published a paper introducing a novel mathematical framework for deterministic, data-driven reachability analysis. The core innovation is the use of Constrained Polynomial Zonotopes (CPZs) to represent both the set of possible system models consistent with observed data and the possible states of the system. This representation solves a key algebraic limitation of previous methods (like standard zonotopes), where multiplying a model set by a state set required over-approximation, introducing 'conservatism' or unnecessary safety margins.
By enabling exact algebraic operations within the CPZ representation, the new method propagates uncertainty through time without this built-in approximation error. This is crucial for verifying the safety of systems with complex, nonlinear (polynomial) dynamics, where reachable sets can be nonconvex shapes. The framework also includes an online refinement scheme that tightens the model set as new data arrives, improving accuracy over time. Numerical examples show the method achieves a 'significant reduction in conservatism' compared to current state-of-the-art techniques, meaning safety guarantees can be both stricter and more accurate.
- Introduces Constrained Polynomial Zonotopes (CPZs) for exact algebraic set propagation, removing a key source of over-approximation error.
- Enables reachability analysis for systems with unknown dynamics and nonconvex reachable sets using only observed data.
- Extends framework to polynomial system dynamics and includes an online scheme to refine models with new data, progressively tightening safety bounds.
Why It Matters
Enables more precise safety verification for AI-controlled physical systems like robots and autonomous vehicles, leading to safer and potentially more capable deployments.