Distributed control of interconnected Chemical Reaction Networks with delay

Abstract This paper introduces a control approach for a class of Chemical Reaction Networks (CRNs) that are interconnected through a delayed convection network. First, a control-oriented model is proposed for interconnected CRNs. Second, based on this model, a distributed control method is introduced which assures that each CRN can be driven into a desired fixed point (setpoint) independently of the delay in the convection network. The proposed algorithm is also augmented with a disturbance attenuation term to compensate the effect of unknown input disturbances on setpoint tracking performance. The control design applies the theory of passive systems and methods developed for multi-agent systems. Simulation results are provided to show the applicability of the proposed control method.

[1]  G. Szederkényi,et al.  Approximation of delayed chemical reaction networks , 2018, Reaction Kinetics, Mechanisms and Catalysis.

[2]  Eduardo D. Sontag,et al.  Synchronization of Interconnected Systems With Applications to Biochemical Networks: An Input-Output Approach , 2009, IEEE Transactions on Automatic Control.

[3]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[4]  Shichao Xu,et al.  Distributed control of plant-wide chemical processes with uncertain time-delays , 2012 .

[5]  Arjan van der Schaft,et al.  A network dynamics approach to chemical reaction networks , 2015, Int. J. Control.

[6]  M. Feinberg.  Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems , 1987 .

[7]  W. Haddad,et al.  Nonnegative and Compartmental Dynamical Systems , 2010 .

[8]  Gábor Szederkényi,et al.  Kinetic feedback design for polynomial systems , 2016 .

[9]  A. Y. Pogromski,et al.  Passivity based design of synchronizing systems , 1998 .

[10]  Gábor Szederkényi,et al.  A model structure-driven hierarchical decentralized stabilizing control structure for process networks , 2014 .

[11]  M. Roussel.  The Use of Delay Differential Equations in Chemical Kinetics , 1996 .

[12]  Gheorghe Craciun,et al.  Toric Differential Inclusions and a Proof of the Global Attractor Conjecture , 2015, 1501.02860.

[13]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

[14]  R. Jackson,et al.  General mass action kinetics , 1972 .

[15]  Gábor Szederkényi,et al.  Semistability of complex balanced kinetic systems with arbitrary time delays , 2017, Syst. Control. Lett..

[16]  Mark W. Spong,et al.  On synchronization of networked passive systems with time delays and application to bilateral teleoperation , 2005 .

[17]  Panagiotis D. Christofides,et al.  Distributed model predictive control: A tutorial review and future research directions , 2013, Comput. Chem. Eng..

[18]  Gábor Szederkényi,et al.  Process Control Based on Physically Inherent Passivity , 2007 .

[19]  Kendell R. Jillson,et al.  Process networks with decentralized inventory and flow control , 2007 .

[20]  David Angeli,et al.  A tutorial on Chemical Reaction Networks dynamics , 2009, 2009 European Control Conference (ECC).

[21]  David F. Anderson,et al.  A Proof of the Global Attractor Conjecture in the Single Linkage Class Case , 2011, SIAM J. Appl. Math..

[22]  Katalin M. Hangos.  Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics , 2010, Entropy.

[23]  Panagiotis D. Christofides,et al.  Selection of control configurations for economic model predictive control systems , 2014 .

[24]  F. Horn.  Necessary and sufficient conditions for complex balancing in chemical kinetics , 1972 .

[25]  Jan Lunze,et al.  Feedback control of large-scale systems , 1992 .

[26]  Michael Baldea,et al.  Dynamics and control of chemical process networks: Integrating physics, communication and computation , 2013, Comput. Chem. Eng..

[27]  Sergio Grammatico,et al.  Multivariable constrained process control via Lyapunov R-functions , 2012 .

[28]  Gabriele Pannocchia,et al.  Parsimonious cooperative distributed MPC algorithms for offset-free tracking , 2017 .

[29]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .

[30]  Murat Arcak,et al.  Networks of Dissipative Systems , 2016 .

[31]  Sigurd Skogestad,et al.  Plantwide control: the search for the self-optimizing control structure , 2000 .

[32]  Maya Mincheva,et al.  Graph-theoretic methods for the analysis of chemical and biochemical networks. II. Oscillations in networks with delays , 2007, Journal of mathematical biology.

[33]  S. Bhat,et al.  Modeling and analysis of mass-action kinetics , 2009, IEEE Control Systems.

[34]  A. Alonso,et al.  Reaction kinetic form for lumped process system models , 2013 .

[35]  G. Szederkényi,et al.  Finding complex balanced and detailed balanced realizations of chemical reaction networks , 2010, 1010.4477.

[36]  Lubomír Bakule,et al.  Decentralized control: An overview , 2008, Annu. Rev. Control..