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SUMMARY:Energy Based Mathematical Modeling\, Simulation\, and Control of E
 nergy Networks - Volker Mehrmann (Technische Universität Berlin)
DTSTART:20230323T150000Z
DTEND:20230323T160000Z
UID:TALK198820@talks.cam.ac.uk
DESCRIPTION:Many real world energy networks consist of subsystems from dif
 ferent physical domains\, modelled by partial-differential equations\, ord
 inary differential equations\, and algebraic equations\, combined with inp
 ut and output connections. To deal with such complex systems\, in recent y
 ears the class of dissipative port-Hamiltonian (pH) descriptor systems has
  emerged as a very successful modeling methodology. The main reasons are t
 hat the network based interconnection of pH systems is again pH\, Galerkin
  projection in PDE discretization and model reduction preserve the pH stru
 cture and the physical properties are encoded in the geometric properties 
 of the flow as well as the algebraic properties of the equations. Furtherm
 ore\, dissipative pH system form a very robust representation under struct
 ured perturbations and directly indicate Lyapunov functions for stability 
 analysis.\nAnother advantage of energy based modeling via pH systems is th
 at each seperate model of a physical systen can&nbsp\; be a whole model ca
 talog from which models can be chosen in an adaptive way within simulation
  and optimization methods.\nWe discuss the class of constrained pH systems
  and illustrate how many classical real world mathematical models can be f
 ormulated in this class.&nbsp\;\nWe illustrate the results with some real 
 world examples from gas transport and district heating systems and point o
 ut emerging mathematical challenges in particular in data based approaches
 .
LOCATION:Seminar Room 2\, Newton Institute
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