Computation of optimal control policy with singular subarc

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Abstract
Singular subarcs appear in the solution of an optimal control problem when one or more of the control variables appear linearly in both the performance index and differential constraint equations or just in the constraint equations. In such cases, the Pontryagin's(1) Maximum Principle yields no information regarding the possible candidates for such subarcs to be optimal trajectories, since the associated Hamiltonian is also linear in the control variables. In the chemical engineering literature such problems have been reported, for instance, in the optimal control of a continuous stirred reactor(2,3,4) in the optimally distributed feed reactors(5), in the optimal catalyst distribution along a tubular reactor(6,7) and in the optimal design of a plug flow tubular reactor(8).