Automatic synthesis for simultaneous supervision and control-a first example

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 can improve the computational performance 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 Grobner bases. The resulting controller description is suited for red 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