METEOR – DFG Research Training Group

Motivation

Research focus at ITR

Our contribution to the project involves integrating control-theoretic guarantees for stability, safety and robustness into data-driven frameworks to manage complex dynamical systems. The focus is on the development of uniform error bounds for Gaussian Process (GP) regressions to provide formal certificates in safety-critical applications. By leveraging Lyapunov-based methods and Control Barrier Functions, we ensure that learning systems can adapt online while strictly adhering to predefined safety constraints. Furthermore, we use operator-theoretic representations, particularly through Koopman operator theory, to identify linear embeddings for nonlinear dynamics and enable the use of efficient optimal control techniques in highly uncertain environments.

Control-Augmented Diffusion for Safety and Dynamical Consistency

We investigate the integration of safety and physical consistency constraints within generative diffusion models used for robotic and autonomous systems. While standard diffusion models excel at high-quality sample generation, they often produce trajectories that violate physical laws or safety boundaries. This research addresses these challenges by augmenting the reverse Stochastic Differential Equation (SDE) of the diffusion process with a virtual control input. This input acts as a guidance mechanism, transforming the generative process into a stochastic control problem. By employing prescribed-time control barrier functions, we induce intermediate samples to return to safe regions, aiming for a probabilistic safety guarantee of the final generated state. The focus is on designing virtual controls that gradually enforce invariance conditions without compromising the expressivity of the generative model.

Interpretable and Uncertainty-Aware Models for Dynamical Systems

We are developing a novel class of transformation models designed for continuous-time and functional data in dynamical systems. Traditional machine learning approaches often rely on parametric assumptions to model aleatoric uncertainty, which may not align with real-world sensor data. We explore distributional regressions that are equivalent to inverse conditional flows to provide interpretable models with rigorous statistical guarantees. The research focuses on formulating continuous-in-time transformation models using differential equations, analogous to normalising flows, and deriving statistical inference for the associated parameter flow. By applying these models to robotic systems, we seek to accurately quantify both epistemic and aleatoric uncertainty. This enables the creation of intelligible models that explain the underlying physics of a system while maintaining the flexibility to capture complex, time-varying data distributions.

ITR team members

• Sandra Hirche (principal investigator)

• Hannes Petrenz

   

Project information