Global controllability between steady supercritical flows in channel networks

Abstract

SUMMARYWe consider a tree-like network of open channels with out ow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the ow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in ÿnite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of C 1 -functions, so no shocks occur.

Existence of classical solutions and feedback stabilization for the flow in gas networks

“…In fact, for the Saint-Venant equations the source term has a more complex structure than for the system studied in this paper which leads to different stationary states, see [16]. For the water flow in channel networks, also supercritical flow is of interest, see [17].…”

Control of Continuum Models of Production Systems

“…Our formal approach allows us to deal with jumps in the initial and boundary values as well as with the nonlocality in the flux function. Alternative approaches to controlling hyperbolic systems [18]- [20] are based on classical solutions and due to the nonlocal term in the flux they are not applicable to our system. For the same reason the recent results due to Bressan et al on optimality conditions [12] are also not directly applicable.…”

Numerical Feedback Stabilization with Applications to Networks

“…Further work also includes hyperbolic systems with source terms (so-called balance laws) for special applications such as gas dynamics [16][17][18] or water flow in open canals [19][20][21][22][23]. To the best of our knowledge only a few results are available, where these kinds of control problems are analyzed from a numerical point of view; see [24,25].…”