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- W2053038308 abstract "An abstract control system is described in a triple ( X, U, φ ) denoting the state set, the input set, and the state transition φ: X × U → X , respectively, which is handled as (i) an algebra consisting of a carrier set X equipped with a set of unary operations φ (−, u ): X → X, u ε U , or as (ii) a relational system of a carrier set X with a binary relation Φ ⊂ X × X , where ( x, x 1 ) ε Φ if there exists u ε U satisfying x 1 = φ ( x, u ). The former standpoint is merely algebraic and intensive studies on its structures such as homomorphisms and congruences are exhausted in the setting of universal algebra. The purpose of this article is to establish a unified way of treating the above two points of view and to characterize a basic control concept, feedback as an intermediate object connecting those two, which is shown to be an abstract extension of the linear geometric approach." @default.
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- W2053038308 date "1981-10-01" @default.
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- W2053038308 title "Homomorphisms and congruences for abstract feedback systems" @default.
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- W2053038308 doi "https://doi.org/10.1016/s0019-9958(81)90066-8" @default.
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