Controlled Invariance and Dynamic Feedback for Systems over Semirings

Abstract

The concept of (A, B)-invariant subspace is the fundamental concept of the geometric approach of control design. It has been extended by many authors to that of (A, B)-invariant module or semimodule, for the sake of extending the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems over semirings, and it is shown that an (A, B)-invariant semimodule over a commutative semiring can be made invariant for the closed-loop system by dynamic feedback.

HVLV Manufacturing System Controlled with Heijunka-Kanban: A Simulation Study of Dead Time and Delay Constraints

“…Its aim is to illustrate that the design problem of a Kanban controlled industrial plant is not straightforward when considering additional delays in the loop. We remark that the delay η and the size limit of the decision step Ωmax act together as a feedforward controller, see [18], [19] for details.…”

Synchronization and Subsynchronization Problems for Switching Max-Plus Systems: Structural Solvability Conditions

“…holds and the last summand of the right-hand term of (12) does not interfere with the state of the system, that evolves, for all k ∈ N, inside V σ(k) ⊆ K σ(k) . Therefore, y P (k) = y M (k) for all k ∈ N.…”

“…Assume that the FSSP is solved by a control law of the form (5). Then, the family of sets of reachable states for the dynamics (12) indexed by the last active mode σ(k) is an (A Eσ , B 1σ )-invariant family of semimodules of feedback type contained in K σ , whose elements contain all the columns of the matrix…”