Learn more by participating in our upcoming workshop on Data-Driven Invariance at CDC 2025!
In recent years, big-data and machine learning have revolutionized numerous fields and industries, but their impact on control design has been less pronounced due to our field’s long and successful pre-existing history with data-driven design in the form of system identification, wherein a model is learned from data and used for model-based controller synthesis. While control theorists have begun to investigate direct data-driven synthesis that skips system identification, we aim to confront the as-yet unmet need for safety.
Invariant sets are the fundamental mathematical construct that scaffolds virtually all safe control, and our work aims to verify and identify invariant sets of autonomous systems, and design controllers to create those invariant sets, using data directly. The remarkable finding so far is that the data-driven perspective can actually be helpful even when a model is available; model-based methods have long-faced computational difficulties for nonlinear systems or non-convex constraints, but our data-driven methods incorporate them seamlessly!
We have studied several ways to compute invariant sets from data, which include designing kernel-based and piecewise affine control barrier functions, which are distinguished among the current literature by establishing deterministic invariance guarantees. However, while virtually all of the field focuses on using data to synthesize barrier functions, we have explored the unique tactic of verifying invariance directly through set operations. A unifying and key goal within this work is to avoid conservative, Lyapunov-like requirements that implicitly require knowledge of a system’s equilibria and exclude key problems involving limit cycles, or stabilization to the feasibility boundary.
Data Driven Invariance Workshop
The data-driven synthesis of invariant sets is a rapidly evolving area due to its deep importance to the safety of learned controllers. We’re organizing a workshop to bring together the community studying this key area, and to help others holistically understand the state-of-the-art. To attend or participate, check out our website or register here.