Robust Deterministic Abstractions of Discr.-Time Cont.-State Systems through Linear State Feedback

Speaker:
Goran Frehse (ENSTA, Institut Polytechnique de Paris, France)
Abstract:
In this seminar, we present a novel method for constructing discrete abstractions for discrete-time, continuous-state systems. Traditional approaches focus on building a discrete bisimulation that represents all possible combinations of states and inputs. This results in highly complex models due to the need to account for all possible behaviors. Instead, we propose to relax the requirement of completeness in order to obtain models that are deterministic, and this readily realizable, and less complex. Our method strikes a balance between system granularity and computational efficiency. Furthermore, we leverage linearization and linear feedback control, which allows us to treat systems exhibiting sufficiently contractive cycles, while related approaches are limited to globally contractive systems. We demonstrate the utility of our approach through numerical experiments, highlighting its applicability in domains where properties such as safety and reversibility are critical.
This work with Gwendal Priser and Elena Vanneaux has been published at Reachability Problems 2024.