Predictive Control with terminal constraint for 2×2 hyperbolic systems of conservation laws

This paper presents a Receding Horizon Optimal Control (RHOC) scheme with zero terminal constraint, to guarantee the stability of linear 2×2 hyperbolic systems with boundary control. The boundary control problem is first reformulated into the abstract form in which the existence and the explicit formulation of the optimal control were established in the literature. These results are then applied in the RHOC scheme to give a complete proof of stability of the closed-loop system. For the implementation, the calculus of variation approach is used to derive the adjoint state which will be discretized and solved with the state to obtain the optimal control. It turns out that this optimal solution is a function of the state and can be implemented in a feedback form. Finally, a simulation is carried out to validate the here-proposed approach.