**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Thursday, January 19, 2023 — 2:00 PM EST

MS Teams: Please email amgrad@uwaterloo.ca for the meeting link

Thanin Quartz | Applied Mathematics, University of Waterloo

Data-Driven Methods for System Identification and Lyapunov Stability

This thesis focuses on data-driven methods applied to system identification and stability analysis of dynamical systems. In the first major contribution of the theorem we propose a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller. The SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. We provide theoretical guarantees of the proposed learning framework in terms of the closed-loop stability for the unknown nonlinear system. We illustrate the effectiveness of the approach with a set of numerical experiments. We then examine another popular data driven method for system identification involving the Koopman operator. Methods based on the Koopman operator aim to approximate advancements of the state under the flow operator by a high-dimensional linear operator. This is accomplished by the extended mode decomposition (eDMD) algorithm which takes non-linear measurements of the state. Under the suitable conditions we have a result on the weak convergence of the eigenvalues and eigenfunctions of the eDMD operator that can serve as components of Lyapunov functions. Finally, we review methods for finding the region of attraction of an asymptotically stable fixed point and compare this method to the two methods mentioned above.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.