Optimization-based design of kinetic feedbacks for nonnegative polynomial systems

Szederkényi, Gábor; Lipták, György; Rudan, János; Hangos, Katalin M.

doi:10.1109/icccyb.2013.6617563

Cited by 7 publications

(9 citation statements)

References 19 publications

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“…In our procedure for removing virtual vertices, deficiency always decreases. This is similar to a result obtained in [48], where the removal of additional monomials that function as controls in a feedback system also lead to a decrease in deficiency. Theorem 4.12.…”

Section: Connection To Deficiency Theorysupporting

confidence: 88%

“…In recent years, the engineering community has utilized properties of mass-action systems in novel ways to designing and analyzing control systems [4,36,44,48]. For example, the controllers can be added in such a way that the resulting system is a complex-balanced mass-action system; from this, one can conclude that the control system has a unique positive steady state and local stability [36,48].…”

Section: Complex-balancing Without Additional Verticesmentioning

confidence: 99%

“…Therefore, if a system is generated by a network that does not enjoy a specific graphical property (e.g., not weakly reversible), we can ask whether the same system may be generated by a weakly reversible network. Others have asked this question before and formulated algorithms for a given number of complexes [34,42,46,47] and applied the results to designing control systems [44,48]. In order to determine whether a given system is generated by a weakly reversible or complex-balanced system, one would have to determine if it can be done using n number of complexes for all n ≥ 1.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems

Crăciun¹,

Jin²,

Yu³

2020

SIAM J. Appl. Math.

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Very often, models in biology, chemistry, physics and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction networks. On the other hand, networks with special properties (such as reversibility or weak reversibility) are known or conjectured to give rise to dynamical systems that have special properties: existence of positive steady states, persistence, permanence, and (for well-chosen parameters) complex balancing or detailed balancing. These last two are related to thermodynamic equilibrium, and therefore the positive steady states are unique and stable. We describe a computationally efficient characterization of polynomial or powerlaw dynamical systems that can be obtained as complex-balanced, detailed-balanced, weakly reversible, and reversible mass-action systems. redirect the reaction z → y * . Instead of the reaction z → y * with flux J z→y * , we have M reactions z → y j with fluxes J ′ z→y j = J y * →y j . Let (G ′ , J ′ ) denote this newest flux system. Recall that flux equivalence means Equation (11) holds at each vertex of G and G ′ . Here we only need to look at the vertex z to show that (G ′ , J ′ ) ∼ (G, J ). Note that y j − z = w j − w 0 . From P (G,J) (y * ) = 0, we also have M j=1 J y * →y j = J z→y * . Thus, the weighted sum of vectors coming out of z isFinally, we prove that the potentials are unchanged. Trivially P (G,J ) (y * ) = P (G ′ ,J ′ ) (y * ) = 0. Also P (G,J) (y j ) = J y * →y j = J ′ z→y j = P (G ′ ,J ′ ) (y j ) for j = 1, 2, . . . , M . Last but not least,J y * →y j = J z→y * = −P (G,J) (z).We have shown that the resulting flux system (G ′ , J ′ ) is flux equivalent to the original flux system (G, J ), and the potential at each vertex is preserved.Remark. In Lemma 4.3, the source vertex z may not be distinct from y j .

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Section: Connection To Deficiency Theorysupporting

confidence: 88%

Section: Complex-balancing Without Additional Verticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems

Crăciun¹,

Jin²,

Yu³

2020

SIAM J. Appl. Math.

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“…Based on constructing the so-called canonical realization of a kinetic system [17], we can give a simple method to generate matrix Y (and thus ψ 2 given by such monomials that do not appear in (16)) using the monomials of the open loop system as as described in [15]. After constructing Y , the kinetic property, minimal deficiency and weak reversibility of the controlled system can be achieved if the MILP problem defined by (11)- (14) and (15) …”

Section: B Static Feedback Designmentioning

confidence: 99%

“…In [15], the problem of obtaining a kinetic closed loop system was addressed in the framework of mixed integer linear programming. In this contribution, the deficiency of the preferably weakly reversible closed loop system is also minimized that is practically more interesting and, at the same time, a more complex computational task.…”

Section: Introductionmentioning

confidence: 99%

Kinetic feedback computation for polynomial systems to achieve weak reversibility and minimal deficiency

Lipták

Szederkényi

Hangos

2014

2014 European Control Conference (ECC)

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Abstract-In this paper, an optimization based state feedback design is proposed for polynomial models that transforms an open-loop system into weakly reversible kinetic form with minimal deficiency, if possible. Therefore, the suggested method is able to decide whether the deficiency zero property and weak reversibility of the closed loop system (that guarantees a robust stability property) is achievable by the given feedback structure. The approach integrates feedback design and previous computational methods for computing dynamically equivalent realizations of kinetic systems. The method assumes a linear input structure of the open loop system, and uses a polynomial feedback constructed from the monomials of the original system possibly extended by new ones. The proposed method is illustrated on two simple examples.

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Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective

Craciun,

Deshpande,

Jin

2023

J Math Chem

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Optimization-based design of kinetic feedbacks for nonnegative polynomial systems

Cited by 7 publications

References 19 publications

An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems

An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems

Kinetic feedback computation for polynomial systems to achieve weak reversibility and minimal deficiency

Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective

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