Abstract
The greatest solution of an inequality KX X LX to solve the optimalcontrol problem for P-Temporal Event Graphs, which is to nd the optimal control thatmeets the constraints on the output and constraints imposed on the adjusted model prob-lem (the model matching problem). We give the greatest solution K X X L Xand X H with K; L;X;H matrices whose are entries in a complete idempotent semir-ings. Furthermore, the authors examine the existence of a sucient condition of theprojector in the set of solutions of inequality K X X L X with K; L;X matrixwhose entries are in the complete idempotent semiring. Projectors can be very necessaryto synthesize controllers in manufacturing systems that are constrained by constraintsand some industrial applications. The researcher then examines the requirements forthe presence of the greatest solution was called projector in the set of solutions of theinequality K X X L X with K; L;X matrices whose are entries in an completeidempotent semiring of interval. Researchers describe in more detail the proof of theproperties used to resolve the inequality K X X L X. Before that, we givethe greatest solution of the inequality KX X LX and X G with K; L;X;Gmatrices whose are entries in an complete idempotent semiring of interval
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