Flow control in gas networks: Exact controllability to a given demand

Abstract

We consider a network of pipelines where the flow is controlled by a number of compressors. The consumer demand is described by desired boundary traces of the system state. We present conditions that guarantee the existence of compressor controls such that after a certain finite time the state at the consumer nodes is equal to the prescribed data. We consider this problem in the framework of continuously differentiable states. We give an explicit construction of the control functions for the control of compressor stations in gas distribution networks.

Exact boundary controllability of nodal profile for quasilinear hyperbolic systems in a tree-like network

“…In practical applications, the nodal profile can be given on one or several simple nodes, and(or) on the multiple node [12]. Similar to Section 2, we give some typical definitions on the exact boundary controllability of nodal profile in a star-like network as follows.…”

“…Recently, for the purpose of some practical applications, a new kind of exact boundary controllability, namely, the exact boundary controllability of nodal profile, was studied for quasilinear hyperbolic systems in [12,13]. Different from the usual exact boundary controllability that asks the solution to the system under certain boundary controls to meet a given final state at a suitably large time t = T, the exact boundary controllability of nodal profile requires that the value of solution satisfies the given profiles on one or several nodes for t T. In [13], the author gave a constructive method to deal with the exact boundary controllability of nodal profile for general one-dimensional quasilinear hyperbolic systems with general nonlinear boundary conditions in the neighbourhood of an equilibrium.…”

Exact boundary controllability of nodal profile for 1-D quasilinear wave equations

“…(ii) We change the role of t and x, and consider a leftward mixed initialboundary value problem on the domain R(T ) for equation (1) with the initial condition…”

“…Recently, promoted by some practical applications, Gugat et al [1] proposed another kind of exact boundary controllability. Different from the usual exact boundary controllability, this kind of controllability, called the nodal profile control, does not ask the solution to exactly attain any given final state at a suitable time t = T by means of boundary controls, instead, it asks the solution to exactly satisfy any prescribed profile on one or some nodes after a suitable time t = T by means of boundary controls.…”

A constructive method to controllability and observability for quasilinear hyperbolic systems

“…Exact boundary controllability of nodal profile. Recently, stimulated by some practical applications, Gugat et al [10] proposed another kind of exact boundary controllability, called the nodal profile control. Different from the usual exact boundary controllability, this kind of controllability does not ask to exactly attain any given final state at a suitable time t = T by means of boundary controls, instead it asks the state to exactly fit any given profile on one or some nodes after a suitable time t = T by means of boundary controls.…”