:Relationship between General Systems and Stationary Systems

概要

論文の詳細を見る
This paper is motivated by the following two basic questions:1. Given a time variant dynamical model z=f(t, z, x) and y=g(t, z) where x, y and z are input, output and state variables, respectively, there is a well-known operation to make the model a time invariant system by introducing a new variable u such that the model is reformulated asd/dt(u z)=(1 f(u, z, x)), y=g(u, z)Then, what is a system theoretic significance of this operation?2. Nerode realization is usually understood as an operation to generate a state space representation of an experimental data. If we consider this operation as a transformation of systems, what is a system theoretic significance of this operation?Practical meanings of these operations are clearly different. However, this paper shows that in the category theoretic framework both of these operations can be represented by a functor between the category of causal time systems S and that of causal stationary systems St. This functor F is called stationalization functor. The fundamental property of this functor is that the output system F(S) of a causal time system S is a universal element of the inclusion functor I: St→S. That is, the above two operations can be interpreted as procedures to generate minimal causal stationary models of the original systems and understood as concrete representations of the "inverse function" of the inclusion functor I.
公益社団法人計測自動制御学会の論文