Receding horizon boundary control of nonlinear conservation laws with shock avoidance

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 occurrence of singularities (called shocks) in the domain. We will show that to avoid the shock, a set of constraints on both the control and the state at the boundary has to be fulfilled. 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 finally carried out with the freeway traffic model to demonstrate the effectiveness of the here-proposed control.