研究会 (2015 年 03 月 13 日)

概要

1. 
  A `systems  immersion' (resp. a `dense immersion') from an 
  n-dimensional system, say S1, into another m-dimensional system S2, 
  (with m greater or equal to n) is a smooth map from the domain 
  (resp. the domain with possibly the exception of a zero-measure set) 
  of S1 onto a smooth manifold, say M, included in the domain of S2, 
  such that any trajectory of S2 starting from M includes a trajectory 
  of S1, and all the trajectories of S1 can be generated by 
  trajectories of S2 starting from M. A quadratic immersion is a dense 
  immersion into a quadratic system. The purpose of this seminar is to 
  give an overview of some recently published results on the exact 
  quadratization of nonlinear systems, i.e. the existence of a 
  quadratic immersion for a very large class of nonlinear systems, so 
  large to include at least all analytic systems. The theory presented 
  follows the same motivation as some classics in nonlinear control, 
  such as the exact linearization: even though the method used for 
  quadratization is independent of it, nonetheless it shares with 
  linearization a type of approach based on reducing the intrinsic 
  complexity of a nonlinear system by means of `simplifying' 
  transformations. In the second part of the seminar examples will be 
  shown where the quadratic immersion can be used for solving basic 
  problems in nonlinear control, such as exponential  stabilization, 
  at least in particular cases of interest in the control practice. 

 Speaker's biographcal sketch: 

  Dr. Francesco Carravetta graduated in Electronic Engineering in 1988 
  (summa cumlaude) at the University of Arcavacata (Italy). After 
  graduated he served as an engineer at Selenia S.p.A Industrie 
  Elettroniche Associate, Roma, and at the research laboratory of 
  Alcatel S.p.A., Speech processing division, Pomezia (Roma) Italy. In 
  1996 he obtained the PhD in Systems Engineering at the University 
  'La Sapienza' of Rome. He is at present Research Scientist at the 
  Institute of Systems Analysis and Informatics (IASI) of the Italian 
  National Research Council. He held visiting positions at the 
  Department of Mathematics of the University of Virginia, 
  Charlottesville, USA, and at the School of Electrical and Electronic 
  Engineering of the University of Adelaide, Adelaide SA, Australia. 
  His main research interests are in the fields of signal processing, 
  filtering and identification, stochastic Control, optimal Control, 
  time delay systems and nonlinear control. 

2. 

  More than 120 years after their introduction, Lyapunov's so-called 
  First and Second Methods remain the most widely used tools for 
  stability analysis of nonlinear systems.  Loosely speaking, the 
  Second Method states that if one can find an appropriate Lyapunov 
  function then the system has some stability property.  A particular 
  strength of this approach is that one need not know solutions of 
  the system in order to make definitive statements about stability 
  properties.  The main drawback of the Second Method is the need to 
  find a Lyapunov function, which is frequently a difficult task. 
  Converse Lyapunov Theorems answer the question: given a particular 
  stability property, can one always (in principle) find an 
  appropriate Lyapunov function?  In this seminar we will survey the 
  history of the field and describe several such Converse Lyapunov
  Theorems for both continuous and discrete-time systems.

 Speaker's biographcal sketch: 

  Dr. Christopher M. Kellett received the Bachelor of Science in 
  Electrical Engineering and Mathematics from the University of 
  California, Riverside and the Master of Science and Doctor of 
  Philosophy in Electrical and Computer Engineering from the 
  University of California, Santa Barbara. He subsequently held 
  research positions with the Centre Automatique et Systemes at 
  Ecole des Mines de Paris, the Department of Electrical and 
  Electronic Engineering at the University of Melbourne, Australia, 
  and the Hamilton Institute at the National University of Ireland, 
  Maynooth. Since 2006, A/Prof. Kellett has been with the School of 
  Electrical Engineering and Computer Science at the University of 
  Newcastle, Australia where he is currently an Australian Research 
  Council Future Fellow.  In 2012, A/Prof. Kellett was awarded a 
  Humboldt Research Fellowship funded by the Alexander von Humboldt 
  Foundation, Germany. Also in 2013 I was one of eight Australian 
  researchers selected for the Emerging Research Leaders Exchange 
  Program supported by the Australian Academy of Technological 
  Sciences and Engineering, the Engineering Academy of Japan, and 
  the Japanese Society for the Promotion of Science. My primary 
  research interests are in the area of systems and control with 
  additional interests in communication and information theory and 
  power systems.

3. 

  The sliding mode controller is a class of variable structure control, 
  which has been successfully implemented in many electromechanical 
  systems for improving their performance and achieving robustness 
  against disturbances. The main attractions of sliding mode controller 
  are invariance to matched uncertainties, model order reduction, 
  simplicity in design and robustness against perturbations. Terminal 
  sliding mode control offers superior property such as finite time 
  convergence to desired state, which is lacking in the classical 
  sliding mode. In this seminar I am going to talk about a continuous 
  homogeneous terminal sliding mode algorithm for the uncertain system 
  with relative degree two with respect to output.  It ensures the 
  finite time convergence to the third-order sliding set, using 
  information about the output and its first derivative. The 
  convergence of the above mentioned algorithm is proved using a 
  homogeneous, continuously differentiable, and strict Lyapunov 
  function.