报告题目：     Exponential Stabilization of Nonlinear Systems viaExtended Linearizations

报告人：Dr. Jan Heiland , Max Planck Institute for Dynamics of Complex Technical Systems

时间：2016年9月21日,14:30-15:30

地点：延长校区IV308

主办方：机自学院自动化系

报告摘要：

  In the work presented, we address the issue of driving a nonlinear system into a non attractive steady state.

  We illustrate how a sufficiently smooth nonlinear system that is autonomous and affine in the control u, can be forced into a desired steady state  z* via a nonlinear feedback law that is defined to exponentially stabilize an associated extended linearization or state-dependent coefficient system

x’(t) = A(x(t))x(t) + Bu(t),  x(0) = z*,

where A(x(t)) is a matrix.

  Extending and specifying recent results on stability of time-varying systems, we develop sufficient conditions for the exponential decay of solutions to the extended linearization without an input. We show that if the coefficient matrix, among others, is uniformly stable in a sufficiently large neighborhood of the current state, then the state will eventually decay. Once the system is close to zero, recent results on local stabilization can be applied.

  Based on the theoretical findings, we propose a scheme for continuously updating a given, locally valid Riccati based feedback so that its stabilizing properties are maintained in the course of the state evolution.

报告人简介：

  Dr. Jan Heiland received a Diploma in Technical Mathematics from the TU Berlin, Germany, in 2009. From 2009 to 2013, he worked on his Ph.D. at the TU Berlin, Germany, where he received his Ph.D. in 2013. He was a Student Employee at the department of aerodynamics of Bombardier Transportation. Since 2013, he is Researcher at Max Planck Institute for Dynamics of Complex Systems in Magdeburg.