Szederkényi, Gábor (MTA SZTAKI)

Analysis and control of positive systems using kinetic realizations: dynamics, structure, and optimization

Positive systems, where the positive (or nonnegative) orthant is invariant for the system dynamics, have important significance in such fields where the studied physical variables changing in time and/or in space are naturally positive (e.g. in certain areas of chemistry, biology, economics or even transportation engineering). Chemical reaction networks (CRNs, also called kinetic systems) form an important subclass of polynomial nonlinear models, and are suitable to describe all the important complex dynamical phenomena (such as the stability/instability/multiplicity of equilibrium points, limit cycles, chaotic behavior etc.) in spite of their relatively simple algebraic structure. It is important to note that compartmental models used e.g. in pharmacokinetic or traffic modeling belong to CRNs. In the theory of CRNs, numerous important results and conjectures have appeared in the literature from the 1970's on the relations between the network structure and the qualitative dynamical properties of the CRN. However, it has also been known for long that the network structure corresponding to a given kinetic dynamics is non-unique. It will be shown in the seminar that the existence analysis and computation of network structures having certain preferred properties can be traced back to the solution of suitably constructed (LP and MILP) optimization problems. An important goal of the research is the utilization of the advantageous computational properties of kinetic systems in nonlinear control, therefore the feedback equivalence problem of kinetic systems will also be touched.

References:

[1] Érdi, P. & Tóth, J. Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models, Manchester University Press, Princeton University Press, 1989
[2] Haddad, W. M.; Chellaboina, V. & Hui, Q. Nonnegative and Compartmental Dynamical Systems, Princeton University Press, 2010
[3] Chellaboina, V.; Bhat, S. P.; Haddad, W. M. & Bernstein, D. S. Modeling and Analysis of Mass-Action Kinetics - Nonnegativity, Realizability, Reducibility, and Semistability, IEEE Control Systems Magazine, 2009, 29, 60-78
[4] Johnston, M. D.; Siegel, D. & Szederkényi, G. A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks, Journal of Mathematical Chemistry, 2012, 50, 274-288
[5] Szederkényi, G.; Hangos, K. M. & Tuza, Z. Finding weakly reversible realizations of chemical reaction networks using optimization, MATCH Commun. Math. Comput. Chem., 2012, 67, 193-212

Date: Sep. 30, Tuesday 4:15pm

Place: BME, Main Building „K”, 1st Floor, Room 50

Homepage of the Seminar