Receding Optimal Boundary Control of Non-linear Hyperbolic Systems of Conservation Laws
Résumé
This paper deals with the boundary control for scalar non-linear hyperbolic systems of conservation laws. One of the issues arising from these systems is the formation of the singularities (called shocks) in the domain. We will show that to avoid the shock, a set of constraints for the control and the state at the boundary has to be ful lled. Then, a proof of the exponential stability of the system is established provided that there is no shock and that the state at the boundary is exponentially stable. These conditions are shown to be achieved by the Receding Horizon Optimal Control approach. A simulation is nally carried out with the freeway tra c model to demonstrate the potential of here-proposed control.