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Low-regret control for a fractional wave equation with incomplete data

Abstract : We investigate in this manuscript an optimal control problem for a fractional wave equation involving the fractional Riemann-Liouville derivative and with missing initial condition. For this purpose, we use the concept of no-regret and low-regret controls. Assuming that the missing datum belongs to a certain space we show the existence and the uniqueness of the low-regret control. Besides, its convergence to the no-regret control is discussed together with the optimality system describing the no-regret control.
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Dumitru Baleanu, Claire Joseph, Gisèle Mophou. Low-regret control for a fractional wave equation with incomplete data. Advances in Difference Equations, Springer, 2016, ⟨10.1186/s13662-016-0970-8⟩. ⟨hal-02548520⟩

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