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Entropy-Related Extremum Principles for Model Reduction of Dissipative Dynamical Systems
Entropy 2010, 12(4), 772-797; doi:10.3390/e12040772
Article

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Process Control Research Group, Computer and Automation Research Institute, Kende u. 13-17, 1111 Budapest, Hungary
Received: 23 February 2010 / Revised: 21 March 2010 / Accepted: 23 March 2010 / Published: 8 April 2010
(This article belongs to the Special Issue Entropy in Model Reduction)
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Abstract

In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.
Keywords: reaction kinetic models; structural stability; entropy-based Lyapunov function; reaction graph; model reduction; lumping; quasi steady state; quasi equilibrium; deficiency reaction kinetic models; structural stability; entropy-based Lyapunov function; reaction graph; model reduction; lumping; quasi steady state; quasi equilibrium; deficiency
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hangos, K.M. Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics. Entropy 2010, 12, 772-797.

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