Extensions to the Theory of Optimal Control of Discrete Event Systems
Raja Sengupta, Stéphane Lafortune · Birkhäuser Basel eBooks · 1993
This paper describes new results concerning the optimal control problem (OCP) formulated in [6]. The discrete event system (DES) is modeled as a finite vertex directed graph, denoted by G = , where V G is the finite set of vertices of G, E G the set of directed edges, υ0 the unique initial vertex, and υm the unique terminal vertex; it is also assumed that G has at most one edge between a pair of vertices and that all vertices in G are accessible with respect to υ0 and co-accessible with respect to υm. We call a graph G with such properties an admissible graph. In general we will use the functional notation E f (.) and V f (.) to denote the set of edges and the set of vertices respectively of an admissible graph. Any path on this graph represents a possible behavior of the DES. Intuitively, paths starting at υ 0 and ending at υ m may be viewed as complete or properly terminating behaviors. Accordingly it is assumed that no non-terminating paths are admissible in the controlled behavior. The admissible paths correspond to the language marked by G, denoted by L m (G). In [6] the same problem was treated but with many restrictions on G. Principal amongst these was the requirement that G be acyclic. This critical qualification is now dispensed with albeit with some increase in the computational complexity.