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@PHDTHESIS{Robertz:61055,
      author       = {Robertz, Daniel},
      othercontributors = {Plesken, Wilhelm},
      title        = {{F}ormal computational methods for control theory},
      address      = {Aachen},
      publisher    = {Publikationsserver der RWTH Aachen University},
      reportid     = {RWTH-CONV-122739},
      pages        = {IV, 203 S.},
      year         = {2006},
      note         = {Aachen, Techn. Hochsch., Diss., 2006},
      abstract     = {This thesis treats structural properties of control
                      systems, e.g. controllability and parametrizability of their
                      behavior, from an algebraic point of view. It contributes
                      the following formal computational methods. Janet's
                      algorithm is extended to Ore algebras which are relevant for
                      system theoretic applications. The generalized Hilbert
                      series is introduced, which enumerates a vector space basis
                      of a finitely presented module over an Ore algebra. A method
                      for linearizing differential equations that is independent
                      of any chosen trajectory is presented. This generic
                      linearization results in a system of linear differential
                      equations with non-constant coefficients which are subject
                      to the original nonlinear equations. Therefore, a
                      computational way for dealing with these equations is
                      explained in the framework of jet calculus and differential
                      rings. The algebraic approach to systems theory which is
                      employed in this thesis associates with every linear system
                      a module over a ring which is chosen in accordance with the
                      type of the given equations (e.g. ordinary or partial
                      differential equations, difference equations, retarded
                      differential equations, etc.). The precision in which
                      structural properties of the solution space of the linear
                      system are represented by the module depends on the choice
                      of the space of admissible functions. A faithful
                      correspondence of homological conditions holds for function
                      spaces which are injective cogenerators. In this thesis an
                      injective cogenerator for every Ore algebra which is
                      relevant for the applications to systems theory is
                      presented. The possibility to parametrize the solution
                      spaces of linear systems is investigated more closely. An
                      extension of the established theory to linear systems which
                      are not completely controllable is explained and a method
                      for computing flat outputs of a certain class of linear
                      systems over Weyl algebras is given. The presented theory
                      and formal methods are illustrated on mechanical and
                      chemical engineering systems.},
      cin          = {114410 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)114410_20140620$ / $I:(DE-82)110000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-opus-15866},
      url          = {https://publications.rwth-aachen.de/record/61055},
}