Bi-objective and hierarchical control for the Burgers equation

We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be regarded as a first step in the solution of control problems of this kind for the Navier–Stokes equations.