Automatic Synthesis for Simultaneous Supervision and Control - a First Example

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 Grobner 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 ..