ITN SADCO "Stability analysis via coupled Hamilton-Jacobi equations" (Task 3.1)

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start of the project: 2011 , end of the project: 2014

contract number: 264735-SADCO (grant agreement number)

funding institution: European Commission (EU)

project members

principal investigator

Prof. Dr. Lars Grüne (University of Bayreuth) and Prof. Dr. Fabian Wirth (University of Würzburg)

project members

Dr. Huijuan Li

aims of the project

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, the corresponding decoupling of the related Zubov equation and the application to the stability analysis will be investigated. The relation to a generalization of Zubov’s method for differential games will also be studied.

The project member will participate in the international training network SADCO with the opportunity of extended research stays at universities. The secondment (6 months) will take place in Sapienza - Universita' di Roma in Rome, Italy.

Further information is available:

publications

H. Li, F. Wirth: Zubov's method for interconnected systems - a dissipative formulation
in: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia, Melbourne, Australia, 2012, 8 pages, CD-ROM, Paper No. 184, full paper

Download as PDF (external link)


Chair -

|  University of Bayreuth -