Constrained exact boundary controllability of a semilinear model for pipeline gas flow

Abstract

While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.

Constrained exact boundary controllability of a quasilinear model for pipeline gas flow

“…This paper is motivated by two seminal works in the literature. The first is 7 , which studies the existence of continuous solutions of the semilinear model subject to upper and lower bounds on the pressure and an upper bound on the Mach number of the gas flow, as well as the constrained exact boundary controllability of the system with the same constraints on the pressure and Mach number. The second is 8 , which investigates the existence of semi-global Lipschitz continuous solutions of the initial boundary value problem on networks.…”