Supremum operators and computation of supremal elements in system theory

Constrained supremum and supremum operators are introduced to obtain a gene ral procedure for computing supremal elements of upper semilattices. Exampl es of such elements include supremal (A; B)-invariant subspaces in linear s ystem theory and supremal controllable sublanguages in discrete-event syste m theory. For some examples, we show that the algorithms available in the l iterature are special cases of our procedure. Our iterative algorithms may also provide more insight into applications; in the case of supremal contro llable subpredicate, the algorithm enables us to derive a lookahead policy for supervisory control of discrete-event systems.