Defense: Haddad, S. (AM) - A Geometric Approach for Learning Reach Sets

Reachability analysis is a method to guarantee the performance of safety-critical applications such as automated driving and robotics against dynamic uncertainties. The main object of study is the reach set, defined as the set of states that a controlled dynamical system may reach at a future time, depending on a set-valued evolution of uncertainties. We develop the theory and algorithms for learning the reach sets of full state feedback linearizable systems---an important class of nonlinear control systems, common in vehicular applications such as automobiles and drones. These reach sets, in very general settings, are compact but nonconvex. The new idea we propose is to compute these reach sets in the associated Brunovsky normal coordinates, and then transform the sets back to the original coordinates via known diffeomorphisms. Our algorithms exploit learning-theoretic ideas to provide probabilistic guarantees on the computed sets.
We detail how these geometric results enable the semi-analytical computation of the reach set of any controllable linear time invariant system, as well as the reach sets of full state feedback linearizable systems.
Leveraging an Isomorphism between compact sets and their support functions, we also propose a data-driven method for learning any general compact set.
This is useful for learning compact sets such as reach sets, maximal control invariant sets, region-of-attraction that are related to an underlying nonlinear dynamical system but an analytic model for the dynamical nonlinearities are unavailable.

Event Host: Shadi Haddad, Ph.D. Candidate, Applied Mathematics

Advisor: Abhishek Halder

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Passcode: 391742

Wednesday, December 6, 2023 at 9:00am

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