Optimization in a class of hereditary systems with direct penalization of the initial data†

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Abstract
In this paper the problem of optimal selection of the pair {u, φ} for a class of non-linear systems with finite heredity in both the states and the control is considered. With the initial data {u(t),φ(t;)/tε[α,t0)] directly penalized in the cost functional, a Pontryagintype Maximum Principle is derived. An example illustrates the results.

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