These reports are from the group Control and System Theory (MAS2.2) 
 

• Higher Order Methods for Differential Inclusions
  Sanja Gonzalez Zivanovic and Pieter Collins
  2010, MAC-1010, ISSN 1386-3703
  In this paper, we give a numerical method for computing rigorous over-approximations
  of the reachable sets of differential inclusions. The method gives high-order error bounds
  for single-step approximations, which is an improvement of the rst-order methods previously
  available. By providing improved control of local errors, the method allows for
  accurate computation of reachable sets over longer time intervals.
  We give several theorems for obtaining local errors of different orders. It is easy to
  see that higher order errors (improved accuracy) require approximations that have larger
  number of parameters (reduced efficiency). The question remains as to approximate
  solution (Theorems 9-17) yields the best trade-off between local accuracy and efficiency
  for computing reachable sets. The answer is not straightforward and most likely depends
  on the system itself. In future work, we plan to investigate the efficiency of the algorithm
  on the number of parameters for various examples.
  We have only considered differential inclusions in the form of input-affine systems, and
  give a brief sketch of how these methods can be applied to other classes of system. We
  also plan to provide a more detailed exposition of the method in these cases.
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• Global optimization of rational multivariate functions
  D. Jibetean
  2001, PNA-R0120, ISSN 1386-3711
  The paper deals with unconstrained global minimization of rational functions. A necessary condition is given for the function to have a finite infimum. In case the condition is satisfied, the problem is shown to be equivalent to a specific constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using semi-definite programming. In general, the relaxation will produce a lower bound of the infimum. However, under no degeneracies, it is possible to check whether the relaxation was in fact exact.
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• Modelling and control of cell reaction networks
  S. Jha; J.H. van Schuppen.
  2001, PNA-R0116, ISSN 1386-3711
  The project aims at a study of the nonlinear systems arising in the biochemical processes occuring inside a cell. The cellular regulation has been formulated in the more familiar framework used in control and system theory in terms of inputs as the variables which can be influenced externally. A graph-theoretic approach has been taken to elicit the rich structure of the dynamical systems represented by metabolic pathways inside the cell. Problems of realization, analysis, and control of cell reaction networks are described.
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