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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara
 

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Fall 2007 Seminar Series
Presents
Homothety and Invariance in Approximate Reachability and
Robust Control Synthesis for Linear Discrete Time Systems
Sasa V. Rakovic
ETH Zürich, Switzerland
Friday, December 7, 2007 4:00-5:00pm Harold Frank Hall 1104
Abstract:
The talk discusses the utilization of set invariance and homothety in reachability analysis and ro-bust
control synthesis for linear discrete time systems. In the first part of the talk we re-examine briefly
the minimality and maximality of invariant sets for linear discrete time systems subject to bounded,
additive, uncertainty by utilizing the recent theoretical framework reported by Artstein and Rakovic.
Utilizing set­dynamics induced by the uncertainty set and the underlying dynamics in the state space
we derive an adequate modification of the standard reachability and viability algorithms and, in turn,
obtain a computationally tractable method for the calculation of the outer invariant approximations of
the minimal invariant set as well as the inner invariant approximations of the maximal invariant set.
The offered procedures for the computations of invariant approximations of the minimal and maxi-
mal invariant set are dual to each other. The procedures produce sequences of improving invariant

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics