Automatic Synthesis for SimultaneousSupervision and Control { a

In industry, supervision and control have often been regarded as separate problems, where the supervision problem has been solved in an ad hoc manner. It would be desirable to handle both control and supervision aspects in the design process. In this work we investigate whether it is possible to synthesize the control law for a discrete event dynamic system, using a polynomial representation of the system and controller. By working through a relatively simple example we propose a synthesis method based on the polynomial representation and repeated Grr obner basis computations. The supervisor objective is given in terms of forbidden states and the controller should actively be able to avoid these. We reduce the manifold of solutions by imposing a weighting function on the state space and by proposing a priority among the actuators. In this way we improve the computational performance radically and we can also control the system towards a desired state, which is our control objective. The computational load lies in the design phase where we use Grr obner bases. The resulting controller description is suited for real time applications since the computations needed are evaluations of a limited number of polynomials. During the design phase we also obtain a polynomial describing where in the state space the computed control law is valid. This makes it possible to examine controllability and supervisability of the system.