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Huijuan Li

Huijan is a Chinese PhD student recruited by Universität Bayreuth. She is working on Stability analysis via coupled Hamilton-Jacobi equations and will be seconded to the University of Rome.

 Huijuan Li-1.jpg Huijuan Li - Universität Bayreuth

  • Main host organisations: Universität Würzburg & Universität Bayreuth, Germany
  • Supervisor: Prof. Dr. Fabian Wirth, Universität Würzburg, Germany
  • Co-Supervisor: Prof. Dr. Lars Grüne, Universität Bayreuth, Germany
  • Secondment organisation: Università di Roma - La Sapienza
  • Nationality: Chinese
  • Fellowship duration: October 2011 - June 2014
  • Background: Huijuan holds a Master of Science in Applied Mathematics from the China University of Geosciences (Wuhan) that she obtained in 2011.
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SADCO project subject: Stability analysis via coupled Hamilton-Jacobi equations

Hamilton-Jacobi equations are connected to Lyapunov functions and thus to stability analysis of nonlinear systems. The Zubov equation is a Hamilton-Jacobi partial differential equation which provides a systematic way to characterize Lyapunov functions via optimal control problems. Optimal control and viscosity solution techniques have been used over the past decade to extend the method to both deterministically and stochastically perturbed and controlled systems. It is now revealed as a versatile tool for the stability analysis of nonlinear systems as well as for the computation of stabilizing controllers. However, for large scale systems these equations become difficult to solve both analytically and numerically. Here a decomposition into subsystems and a stability analysis based on a generalized small gain theorem may provide a remedy. In this project area, the corresponding decoupling of the related Zubov equation and the application to the stability analysis will be investigated. Possible generalization of Zubov’s method for differential games will also be studied. 

 

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