<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Control of Conservation Laws – An Application

Department of Automation and Electronics,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Control of Conservation Laws \u2013 An Application"}

We present here three types of controlled boundary value problems for conservation laws arising from energy co-generation, hydraulic flows and water hammer for...

Control of Conservation Laws – An Application

Published Online: Jan 25, 2019

Page range: 155 - 174

Received: Apr 18, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0014

Keywords
nonlinear systems, conservation laws, feedback control, energy identity

© 2018 Vladimir Răsvan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Control of Conservation Laws – An Application

Published Online: Jan 25, 2019

Page range: 155 - 174

Received: Apr 18, 2018

DOI: https://doi.org/10.2478/tmmp-2018-0014

Keywordsnonlinear systems, conservation laws, feedback control, energy identity

© 2018 Vladimir Răsvan, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear systems, conservation laws, feedback control, energy identity