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	The Extension of the Attainable Region Approach for Synthesizing
	Reactors to Allow for Choice of Control Policies
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	S. Godorr, C. McGregor, D. Hildebrandt and D. Glasser 
	
	School of Process and Materials Engineering, 
	University of the Witwatersrand.
	P.Bag 3, WITS 2050, South Africa

	E-Mail Address: 	dihil@chemeng.chmt.ac.za
	Tel No: 		11- 716 2413
	Fax No: 		11- 339 7213

    Abstract:
	Previously the Attainable Region (AR) has been found for systems
	where the rate vector is uniquely defined by the characteristic
	vector. We now examine problems where there is also a free
	parameter, such as temperature or a reactant concentration, which
	also needs to be chosen at each point. This means that the rate
	vector is no longer uniquely defined by the characteristic vector,
	but can take on a range of values for each value of the
	characteristic vector. We derive a set of conditions that need be
	satisfied in order that rate vectors do not point outwards on the
	boundary of the AR. 

	We use these conditions to solve a number of examples. In the
	examples in which mixing does not occur in the boundary of the AR,
	we have shown that the results agree with those derived from
	Pontryagins Maximum Principle. In more general cases we have been
	able to simultaneously generate the optimal reactor structures with
	their associated optimal control policies.