Submodule Construction and Supervisory Control: A Generalization

نویسنده

Gregor von Bochmann

چکیده

We consider the following problem: For a system consisting of two submodules, the behavior of one submodule is known as well as the desired behavior S of the global system. What should be the behavior of the second submodule such that the behavior of the composition of the two submodules conforms to S ?-This problem has also been called "equation solving", and in the context of supervisory control, it is the problem of designing a suitable controller (second submodule) which controls a given system to be controlled (first submodule). Solutions to this problem have been described by different authors for various assumptions about the underlying communication mechanisms and conformance relations. We present a generalization of this problem and its solution using concepts from relational database theory. We also show that several of the existing solutions are special cases of our general formulation 1 Introduction In automata theory, the notion of constructing a product machine S from two given finite state machines S1 and S2, written S = S1 x S2, is a well-known concept. This notion is very important in practice since complex systems are usually constructed as a composition of smaller subsystems, and the behavior of the overall system is in many cases equal to the composition obtained by calculating the product of the behaviors of the two subsystems. Here we consider the inverse operation, also called equation solving: Given the composed system S and one of the components S1, what should be the behavior S2 of the second component such that the composition of these two components will exhibit a behavior equal to S. That is, we are looking for the value of X which is the solution to the equation S1 x X = S. This problem is an analogy of the integer division, which provides the solution to the equation N1 * X = N for integer values N1 and N. In integer arithmetic, there is in general no exact solution to this equation; therefore integer division provides the largest integer which multiplied with *

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