Open dynamical systems and their control
The behavioral approach is followed in this paper and some of the main features of the theory of open dynamical systems are described. Linear time-invariant differential systems receive special attention. Object-oriented mathematical modelling of complex systems leads to a model that relates the variables whose dynamic relation one wants to model (called manifest variables) to auxiliary variables (called latent variables) that have been introduced in the modelling process. By using kernel representations, the manifest behavior and latent variable representations in the linear time-invariant case, the elimination theorem is proved. This theorem means that the latent variables may be eliminated and that the number of equations can be reduced to no more than the number of manifest variables. Again for linear time-invariant differential systems, various equivalences for controllability are proved, anwering questions such as: ''What conditions on the parameters of a system representation imply controllability?'' and ''Do controllable systems admit a particular representation in which controllability becomes apparent?''. The theory of observability, running parallel to that of controllability, is only briefly touched upon in the paper. The paper ends with a discussion of control, which is viewed as system interconnection.
linear time-invariant differential systems
scientific article; zbMATH DE number 1184406