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2.2 the discrete deterministic process

Consider the process illustrated in Fig. 2.1, consisting of R distinct stages.

These will be numbered in the direction opposite to the flow of the process stream, so that stage R is the T stage from the end.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Thus Af denotes the state of the feed to the R-stage process, and Af the state of the product from the last stage.

Each stage transforms the state Af of its feed to the state Af in a way that depends on the operating variables Af.

We write this Af.

This transformation is uniquely determined by Af and we therefore speak of the process as deterministic.

In practical situations there will be restrictions on the admissible operating conditions, and we regard the vectors as belonging to a fixed and bounded set S.

The set of vectors Af constitutes the operating policy or, more briefly, the policy, and a policy is admissible if all the Af belong to S.

When the policy has been chosen, the state of the product can be obtained from the state of the feed by repeated application of the transformation ( 1 ) ; ;

thus Af.

The objective function, which is to be maximized, is some function, usually piecewise continuous, of the product state.

Let this be denoted by Af.