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In this work, we will investigate the question of optimal control forbilinear systems with constrained endpoint. The optimal control will becharacterized through a set of unconstrained minimization problems thatapproximate the former. Then a class of bilinear systems for which the optimalcontrol can be expressed as a time-varying feedback law will be identified.Finally, applications to parabolic and hyperbolic partial differentialequations are provided.

Problem of optimal control for bilinear systems with endpoint constraint