Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference
This work addresses safety verification for systems with hidden states, a common challenge in robotics and control, though it is incremental as it builds on existing barrier certificate methods.
The paper tackles the problem of certifying safety in unknown dynamical systems with latent states and polynomial dynamics by proposing a Bayesian inference approach to synthesize barrier certificates, resulting in probabilistic guarantees for validity as demonstrated in a numerical simulation.
Certifying safety in dynamical systems is crucial, but barrier certificates - widely used to verify that system trajectories remain within a safe region - typically require explicit system models. When dynamics are unknown, data-driven methods can be used instead, yet obtaining a valid certificate requires rigorous uncertainty quantification. For this purpose, existing methods usually rely on full-state measurements, limiting their applicability. This paper proposes a novel approach for synthesizing barrier certificates for unknown systems with latent states and polynomial dynamics. A Bayesian framework is employed, where a prior in state-space representation is updated using output data via a targeted marginal Metropolis-Hastings sampler. The resulting samples are used to construct a barrier certificate through a sum-of-squares program. Probabilistic guarantees for its validity with respect to the true, unknown system are obtained by testing on an additional set of posterior samples. The approach and its probabilistic guarantees are illustrated through a numerical simulation.