Receding Horizon Observer and Control for linear 2×2 hyperbolic systems of conservation laws

This paper presents an infinite-dimensional Receding Horizon Observer for linear 2×2 hyperbolic systems with boundary measurements. The initial state is estimated as the optimal solution of an optimization problem which minimizes the distance between the measurements and the observer output. A constructive method is used to derive the existence and uniqueness of the solution. A composite strategy combining Receding Horizon Optimal Control and Receding Horizon Observer is also presented. Its effectiveness in guaranteeing closed-loop stability is also demonstrated. For the implementation, the calculus of variation approach is used to derive the adjoint state which will be discretized and solved with the observer state to obtain the optimal solution. Finally, a simulation with a linearized model of an open-channel system is carried out to validate the here-proposed approach.