Supervisory control of finite state machines

Abstract

We address a problem of finding a finite state machine (FSM), which composed with a given FSM, satisfies a given specification. The composition we use is the standard synchronous automata composition restricted to cases which correctly model hardware interconnection. For the satisfaction relation, we use language containment. We present a procedure that will generate a solution (if one exists) which is maximal, i.e. contains behaviors of all other solutions.* Supported by SRC under contract 95-DC-324A.

Most General Property-Preserving Updates

“…These results could be exploited both to make our approach more ecient and to extend it to properties that go beyond safety, like liveness and deadlock freedom. Another problem related to ours is supervisory control of discrete event systems (see, e.g., [4]). The main dierence is in the composition mechanism, which features a feedback control loop and introduces latency, while this does not happen in our case.…”

Software monitoring with bounded overhead

“…The classic theory of digital control for linear systems is discussed extensively in [9]. The theoretical treatment of the automatic synthesis of a maximal controller within supervisory control is given in [17,1]. The same is discussed within a timed framework in [17,1].…”

“…• HCSM is formally grounded in control theory, in particular, the theory of supervisory control of finite-state automata [17,1].…”

“…While a linearization is conceivable, for such nonlinear systems a superior approach is provided in the automata-theoretic setting [17,1], where the controller design (synthesis) problem is referred to as supervisory control.…”

“…In this setting, the plant P is a state machine, the desired outcome (tracking the reference input) is a language L, and the controller design problem is that of designing a controller Q, which is also a state machine, such that the language L(Q P ) of the composition of Q and P is included in L. In [17,1] it is shown that this problem is decidable for finite state machines.…”