A note on Nash equilibrium with wave dynamics and boundary control: controllability, observability and stabilizability considerations

ABSTRACT

In this paper, the gas dynamics within the pipelines is written as a wave repetitive process, and modified in a way that the dynamics is driven by the boundary conditions. We study controllability of the system through boundary control and every agent, as well as observability of the system being steered by initial and boundary data. Next, we obtain sufficient criteria for the existence and uniqueness of boundary equilibrium controls. From the point of view of some applications, e.g. in high pressure gas pipeline management, it seems to make sense to consider boundary data controls. The same problem is then extended to its infinite counterpart since it may run infinitely and, in this case, we become interested in studying its stabilisation.

KEYWORDS:

• 2D systems
• boundary control
• difference games
• gas networks modelling
• Nash equilibrium
• repetitive processes

Acknowledgments

The authors would like to thank the reviewers for their comments that helped in improving this document.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and third authors acknowledge Fundação para a Ciência e a Tecnologia (FCT) and COMPETE 2020 program for the financial support to the project UID-EEA-00048-2013. The second author is financed by Portuguese Funds through FCT, within the Project UID/MAT/00013/2013.