Applying Koopman Methods for Nonlinear Reachability Analysis

Applying Koopman Methods for Nonlinear Reachability Analysis

Sweering, Tim (TU Delft Mechanical, Maritime and Materials Engineering)

Mazo, M. (mentor)
Delimpaltadakis, Giannis (mentor)
Lukina, A. (graduation committee)

Delft University of Technology

Mechanical Engineering | Systems and Control

2021-10-05

In this thesis we investigate the possibilities for applying Koopman methods for reachability analysis. Reachability analysis is a verification process used to determine that a dynamical system starting in an initial set X0 cannot reach a certain set of dangerous states D within a time interval [0,T]. Koopman methods seem promising, because they predict nonlinear behaviour using linear techniques. However they have not been widely applied to reachability analysis.

We describe three different Koopman methods: data-driven, Polyflow and Carleman. We use the Polyflow method combined with ideas from several other methods to create a new reachability tool: PolyReach. Next, we analyse the performance of PolyReach by comparing it with a state-of-the-art reachability algorithm Flow* on various nonlinear systems. Finally, we summarize the strengths and weaknesses of the PolyReach tool and discuss ideas for further improvement.

Koopman Operator
Polyflow
Reachability Analysis
Nonlinear dynamics

http://resolver.tudelft.nl/uuid:f69bdabf-6953-4025-b477-9bdd18339408

Student theses

master thesis

© 2021 Tim Sweering