Reports of Control and System Theory

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

  • Higher Order Methods for Differential Inclusions/embrSanja Gonzalez Zivanovic and Pieter Collinsbr2010, MAC-1010, ISSN 1386-3703brIn this paper, we give a numerical method for computing rigorous over-approximationsbrof the reachable sets of differential inclusions. The method gives high-order error boundsbrfor single-step approximations, which is an improvement of the rst-order methods previouslybravailable. By providing improved control of local errors, the method allows forbraccurate computation of reachable sets over longer time intervals.brWe give several theorems for obtaining local errors of different orders. It is easy tobrsee that higher order errors (improved accuracy) require approximations that have largerbrnumber of parameters (reduced efficiency). The question remains as to approximatebrsolution (Theorems 9-17) yields the best trade-off between local accuracy and efficiencybrfor computing reachable sets. The answer is not straightforward and most likely dependsbron the system itself. In future work, we plan to investigate the efficiency of the algorithmbron the number of parameters for various examples.brWe have only considered differential inclusions in the form of input-affine systems, andbrgive a brief sketch of how these methods can be applied to other classes of system. Webralso plan to provide a more detailed exposition of the method in these cases.bra href= the pdf-file/a/li liemspan class=boldGlobal optimization of rational multivariate functions/spanbr/emD. Jibeteanbr2001, PNA-R0120, ISSN 1386-3711brspan class=boldThe 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.bra title=Global optimization of rational multivariate functions href=/system/files/u328/PNA-R0120.pdfDownload the pdf-file/a/span/li liemspan class=boldModelling and control of cell reaction networks/spanbr/emS. Jha; J.H. van Schuppen.br2001, PNA-R0116, ISSN 1386-3711brspan class=boldThe 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.bra title=Modelling and control of cell reaction networks href=/system/files/u328/PNA-R0116.pdfDownload the pdf-file/a/span/li /ul