Sections

WP3 - Stabilisation methods for nonlinear systems

  • State of the art

Hamilton-Jacobi equations are very similar to the equations of Lyapunov stability theory and are thus linked to the 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 - the domain of attraction is then characterized as a sublevel set of this Lyapunov function. Over the last decade, the method has been extended, with the help of both optimal control and viscosity solution techniques, to both deterministically and stochastically perturbed and control systems, and has emerged as a versatile tool, both for the stability analysis of nonlinear systems and also for the computation of stabilizing controllers. However, for large 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 can provide a remedy.

 

  • Objectives

In this WP, the corresponding decoupling of the related Zubov equation and the application to the stability analysis will be investigated. Furthermore, this approach will be extended to allow for constraints on state-variables (presence of obstacles).

 

  • Fellows projects

Name

ER/

ESR 

 Subject  Main host organisation Secondment organisation(s)

Maria Soledad Aronna

 ER Control Theory in Classical Mechanics Univ. Padova Imperial College

Huijuan Li

 ESR Stability analysis via coupled Hamilton-Jacobi equations Univ. Bayreuth Univ. Rome

Vryan Gil Palma

 ESR Robust nonlinear model predictive control  Univ. Bayreuth Imperial College, KU Leuven

Mario Zanon

 ESR Model Predictive and optimal flight control in the presence of inequality constraints KU Leuven

Univ. Bayreuth

 

  • Planned person-months: 108
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