Landry DJOMEGNE : On the multi-objective control of a parabolic equation with boundary controls
The work we present deals with a multi-objective control problem for a parabolic equation with boundary controls. We present a Stackelberg-Nash strategy, which combines the concepts of zero controllability and Nash equilibrium. We assume that the system is influenced by a hierarchy of boundary controls, consisting of a main control (the leader) aimed at driving the solution of the system toward zero at a final time, and a pair of secondary controls (the followers) designed to minimize two prescribed cost functionals while adapting to the leader's objective. The main novelty of this work lies in the fact that all controls are located at the boundary. One of the major difficulties encountered concerns obtaining an appropriate Carleman-type observability inequality for an adjoint system with boundary coupling terms.
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