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Previously, the attainable region has been constructed for systems where the rate vector is uniquely defined. In this paper we extend the attainable region approach to situations where the rate vector depends on a control parameter, such as temperature. In these cases, the rate vector can take on a range of values, depending on the value of the control parameter. Arguments based on the geometry of the boundary of the attainable region are used to derive equations that describe the optimal control policies. These conditions are applied to various examples and both the optimal reactor structures as well as optimal operating and control policies are derived by looking at the structures that make up the boundary of the attainable region. In particular, an example is given where the optimal reactor structure has a reactor with simultaneous side stream addition and temperature control.

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