**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

Friday, September 30, 2022 4:00 PM EDT

MS Teams (please email amgrad@uwaterloo.ca for the meeting link)

Ruikun Zhou | Applied Mathematics, University of Waterloo

Learning-based Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees

Learning for control of dynamical systems with formal guarantees remains a challenging task. Thanks to state-of-the-art machine learning techniques and classical control theories, this issue is being addressed by data-driven control approaches. In this talk, I will present how to learn the unknown dynamics and obtain stability guarantees for nonlinear dynamical systems with two learning-based approaches: neural networks and the Koopman operator.

Frist, I will illustrate 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, where the two different neural networks are responsible for learning the unknown dynamics and identifying a valid Lyapunov function with a provably stabilizing nonlinear controller respectively, while the SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. Next, the proposal on estimating the maximal ROA of nonlinear systems with the Koopman operator and Lyapunov functions will be discussed. The Koopman operator provides a global linear representation of nonlinear systems by mapping it into some infinite-dimensional operator space, where the Koopman eigenfunctions parametrize a pool of Lyapunov function candidates. After being verified by the SMT solver, the sub-level sets of the remaining valid Lyapunov functions depict the estimated ROA. The effectiveness of both approaches is illustrated with numerical experiments on typical nonlinear control problems.

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 co-ordinated within the Office of Indigenous Relations.