Time and Norm Optimality of Weakly Singular Controls
نویسنده
چکیده
Let ū(t) be a control that satisfies the infinite-dimensional version of Pontryagin’s maximum principle for a linear control system, and let z(t) be the costate associated with ū(t). It is known that integrability of ‖z(t)‖ in the control interval [0, T ] guarantees that ū(t) is time and norm optimal. However, there are examples where optimality holds (or does not hold) when ‖z(t)‖ is not integrable. This paper presents examples of both cases for a particular semigroup (the right translation semigroup in L2(0,∞)). Mathematics Subject Classification (2000). 93E20, 93E25.
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