研究会 (2017 年 10 月 30 日)

概要

1. 
  We begin with an analysis of nonlinear observers in terms of passivity. 
  By suitably defining input and output of the estimation error dynamics,
  designing observer injection gain can be viewed as making the error
  dynamics passive. This finding in turn leads to another interpretation 
  of reduced-order observer since the error dynamics of reduced-order 
  observere is nothing but the zero-dynamics of full-order error dynamics. 
  Then, we note that passivity property naturally leads to some 
  robustness, which is, in the case of observer, against measurement 
  disturbance. We will talk about recent results on nonlinear observers 
  robust to measurement disturbance in the ISS (input-to-state stability) 
  sense.

 Speaker's biographcal sketch: 

  Hyungbo Shim received the B.S., M.S., and Ph.D. degrees from Seoul 
  National University, Korea, and held the post-doc position at University 
  of California, Santa Barbara till 2001. He joined Hanyang University, 
  Seoul, Korea, in 2002. Since 2003, he has been with Seoul National 
  University, Korea. He served as associate editor for Automatica, IEEE 
  Trans. on Automatic Control, Int. Journal of Robust and Nonlinear 
  Control, and European Journal of Control, and as editor for Int. Journal 
  of Control, Automation, and Systems. He was the Program Chair of 
  ICCAS 2014 and Vice-program Chair of IFAC World Congress 2008. His 
  research interes includes stability analysis of nonlinear systems, 
  observer design, disturbance observer technique, secure control systems, 
  and synchronization.

2. 
  In this study, a robust Pareto suboptimal strategy for  
  uncertain Markov jump linear stochastic systems (UMJLSSs) with
  multiple decision makers is investigated. A guaranteed cost-control  
  principle is employed to obtain the conditions given using
  a stochastic algebraic Riccati inequality (SARI), such that the  
  closed-loop stochastic system is exponentially mean square stable (EMSS),
  having a cost bound. The minimization problem of the cost bound is  
  formulated, and the necessary conditions, which are obtained via the
  set of cross-coupled stochastic Riccati equations (CCSAREs), are derived  
  with the help of the Karush-Kuhn-Tucker (KKT) conditions.
  Finally, a numerical example is solved to demonstrate the effectiveness  
  and usefulness of the proposed strategy.

3. 
  This talk forces on feedback interconnection of two nonlinear systems. 
  The component systems are assumed to be integral input-to-state 
  stability (iISS). iISS allows the state of a system to be unbounded even 
  for bounded external input, while in contrast, input-to-state stability 
  (ISS) guarantees the state to be bounded. The concept of iISS captures 
  inevitable dynamics arising from saturation and bilinearity. 
  Interestingly, the state going far away can be pulled back by connecting 
  an ISS system to it if the stability of the ISS system is strong enough. 
  A small-gain condition allows one to check if this mechanism kicks in. 
  The small-gain condition is merely a test. Constructing a Lyapunov 
  function of the feedback and investigating its sublevel sets can provide 
  one with useful information of system behavior, One may conjecture that 
  the magnitude of the state increases very large temporarily when 
  stability margins are small. The aim of this talk is to discuss this
  conjecture and correct it. As expected, sublevel sets of a previously 
  available Lyapunov function is flattened extremely when stability 
  margins are small. It is, however, demonstrated that it is not 
  necessary, and a new Lyapunov function producing surprisingly better 
  sublevel sets is proposed.