A way to deal with nonlinear boundary conditions in open-channel optimal control problems

This paper is concerned with the regulation problem of open-channel hydraulic systems. The water flow and level within the reach are controlled through the opening rates of two gates localized at each side of the reach. This problem is a non linear infinite-dimensional boundary control problem. Based on the fact that the dynamics of the sliding gates is far faster than the dynamics of the water flow within the reach, the regulation problem of open-channel hydraulic systems is decoupled into two independent linear problems. As a result, the linear finite-dimensional robust optimal control of the water level and flow within the reach and the linear finite-dimensional tracking problem which concerns the sliding gates are successfully addressed, respectively. Simulations are presented to validate its effectiveness.