999 research outputs found
Computing Dynamic Output Feedback Laws
The pole placement problem asks to find laws to feed the output of a plant
governed by a linear system of differential equations back to the input of the
plant so that the resulting closed-loop system has a desired set of
eigenvalues. Converting this problem into a question of enumerative geometry,
efficient numerical homotopy algorithms to solve this problem for general
Multi-Input-Multi-Output (MIMO) systems have been proposed recently. While
dynamic feedback laws offer a wider range of use, the realization of the output
of the numerical homotopies as a machine to control the plant in the time
domain has not been addressed before. In this paper we present symbolic-numeric
algorithms to turn the solution to the question of enumerative geometry into a
useful control feedback machine. We report on numerical experiments with our
publicly available software and illustrate its application on various control
problems from the literature.Comment: 20 pages, 3 figures; the software described in this paper is publicly
available via http://www.math.uic.edu/~jan/download.htm
Dimension of the solutions space of PDEs
We discuss the dimensional characterization of the solutions space of a
formally integrable system of partial differential equations and provide
certain formulas for calculations of these dimensional quantities.Comment: Contribution to the conference GIFT-200
Finding complex balanced and detailed balanced realizations of chemical reaction networks
Reversibility, weak reversibility and deficiency, detailed and complex
balancing are generally not "encoded" in the kinetic differential equations but
they are realization properties that may imply local or even global asymptotic
stability of the underlying reaction kinetic system when further conditions are
also fulfilled. In this paper, efficient numerical procedures are given for
finding complex balanced or detailed balanced realizations of mass action type
chemical reaction networks or kinetic dynamical systems in the framework of
linear programming. The procedures are illustrated on numerical examples.Comment: submitted to J. Math. Che
Cauchy problem for integrable discrete equations on quad-graphs
Initial value problems for the integrable discrete equations on quad-graphs
are investigated. A geometric criterion of the well-posedness of such a problem
is found. The effects of the interaction of the solutions with the localized
defects in the regular square lattice are discussed for the discrete potential
KdV and linear wave equations. The examples of kinks and solitons on various
quad-graphs, including quasiperiodic tilings, are presented.Comment: Corrected version with the assumption of nonsingularity of solutions
explicitly state
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