Abstract
In this paper a class of input-parametrized bilinear positive systems is considered. This class is characterized by the fact that the input variables affect only the diagonal entries of the dynamical matrix. The class of systems considered is relevant to a variety of dynamical models arising in system biology and compartmental systems. Given a final time tf, it is proven that the any component of the state vector at tf is a convex functional of the input variables. If a linear cost of the final state is considered this result has the important consequence that any Pontryagin solution of the associated optimal control problem is optimal and can be numerically computed by using standard gradient-type algorithms. A few extensions are given and an example is provided to illustrate the theory.
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