Optimal parametric discrete event control: Problem and solution
Christopher H. Griffin · 2008
We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model G defined over an event alphabet Sigma so that the plant model language L = LM(G) is prefix closed. We further assume the existence of a base control structure MK, which may be either a finite state machine or a deterministic pushdown machine. If K = LM(MK), we assume K is prefix closed and that K C L. We associate each controllable transition of MKwith a binary variable X1,..., Xnmiddot indicating whether the transition is enabled or not. This leads to a function MK(X1, ,...,- , Xn), that returns a new control specification depending upon the values of X1,..., Xnmiddot We exhibit a branch-and-bound algorithm to solve the optimization problem minx1x,...xn&maxwwepsiK C(w) such that MK(X1,...,Xn) \= |= and LM(MK(X1,...,- , Xnmiddot)) epsi C(L). Here . is a set of logical assertions on the structure of MK(X1, X1,...,- , Xnmiddot), and MK(X1,...,- , Xnmiddot) \= || indicates that MK(X1,...,- , Xn) satisfies the logical assertions; and, C(L) is the set of controllable sublanguages of L1.