Maximum principle for optimal distributed control of the viscous Dullin–Gottwald–Holm equation

In this paper, the optimal distributed control of the viscous Dullin–Gottwald–Holm equation is investigated. Adopting the Dubovitskii and Milyutin functional analytical approach, we obtain the Pontryagin maximum principle of the system. The necessary optimality condition is established for an optimal control problem in fixed final horizon case. Finally, an illustrative example is also given.