Open AccessControl of Conservation Laws – An Application
Author(s) -
Vladimir Răsvan
Publication year - 2018
Publication title -
tatra mountains mathematical publications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.171
H-Index - 12
eISSN - 1338-9750
pISSN - 1210-3195
DOI - 10.2478/tmmp-2018-0014
Subject(s) - conservation law , mathematics , nonlinear system , boundary (topology) , boundary value problem , lyapunov function , control theory (sociology) , mathematical analysis , control (management) , computer science , physics , quantum mechanics , artificial intelligence
We present here three types of controlled boundary value problems for conservation laws arising from energy co-generation, hydraulic flows and water hammer for hydroelectric power plants and control of the open channel flows (shallow water). The novelty of these models, from the mathematical point of view, is that they are described by nonlinear hyperbolic partial differential equations of the conservation laws with (possibly) nonlinear boundary conditions. At their turn these boundary conditions are controlled by some systems of ordinary differential equations. The engineering requirements for such systems are asymptotic stability and disturbance rejection: these properties have to be achieved by feedback control. In our setting the main tool for tackling these problems is a suitable Lyapunov functional arising from the energy identity. The hints for “guessing” this functional are to be found in the linearized version of the aforementioned mathematical objects.