Boundary control for exact cancellation of boundary disturbances in hyperbolic systems of conservation laws

Robust feedforward boundary control of hyperbolic conservation laws

“…In order to illustrate our approach and to link it with previous results presented by [1], we consider the special case where γ = δ = 0, corresponding to a frictionless horizontal canal. In this case, an analytical expression for open-loop control has been obtained by [1] using a Riemann invariants approach. Our formula (12) does not lead to the same expression.…”

“…Our formula (12) does not lead to the same expression. However, using the explicit frequency domain expression of the feedforward controller (8) and using another series decomposition, we recover the expression of [1]. Moreover, we derive upper and lower bounds for the H ∞ norm of the approximation error due to the infinite series truncation.…”

“…[10,12]) we consider in this paper a more general class of hyperbolic systems, and use a frequency domain approach. This enables us to extend the results of [1] to the case of canal pools with nonzero slope and friction, and arbitrary uniform geometry (not necessarily rectangular). We design a feedforward compensator that perfectly reject the perturbation.…”

“…This open-loop control problem was first considered in [1], where the authors used a Riemann invariants approach to derive 716 X. LITRICO, V. FROMION AND G. SCORLETTI an explicit expression for the open-loop control. The proposed method is however restricted to specific hyperbolic plants corresponding to horizontal frictionless channels.…”

“…Input-output transfer matrix. The open-loop transfer matrix of the plant can be obtained by applying Laplace transform to the linear partial differential equations (1), and solving the resulting system of Ordinary Differential Equations in the variable x, parameterized by the Laplace variable s [9,12]. The downstream water level is then related to upstream and downstream discharges as follows:…”