In: Tatra Mountains Mathematical Publications, vol. 71, no. 1
Vladimir Răsvan
Detaily:
Rok, strany: 2019, 155 - 174
Jazyk: eng
Kľúčové slová:
nonlinear systems, conservation laws, feedback control, energy identity
Typ článku: Mathematics
O článku:
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.
Ako citovať:
ISO 690:
Răsvan, V. 2019. Control of conservation laws an application. In Tatra Mountains Mathematical Publications, vol. 71, no.1, pp. 155-174. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0014
APA:
Răsvan, V. (2019). Control of conservation laws an application. Tatra Mountains Mathematical Publications, 71(1), 155-174. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0014
O vydaní:
Vydavateľ: MÚ SAV
Publikované: 2. 1. 2019