Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation
The authors study a multi-objective control problem for the Kuramoto-Sivashinsky equation following the hierarchical strategy. It is assumed that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. As is known, the Carleman inequalities play an important role in analysis of controllability of distributed systems. The authors prove a new inequality of this type. Then, they establish the observability inequality and deal with the null controllability of the linear system. Finally, it is shown that the optimality system is locally null controllable using a local inversion argument.
scientific article; zbMATH DE number 7041860
scientific article