Hybrid model predictive control of induction of Escherichia coli

Julius, A. Agung; Sakar, Mahmut Selman; Bemporad, Alberto; Pappas, George J.

doi:10.1109/cdc.2007.4434840

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…Hybrid systems have been used to describe many different situations, see for instance [4]. Very close to our framework are [13], and the late work by Gillespie [9]. Note that in our framework the dynamics of both the discrete and the continuous state spaces have in principle a similar mathematical description.…”

Section: Introductionmentioning

confidence: 82%

An Averaging Principle for Combined Interaction Graphs — Connectivity and Applications to Genetic Switches

Kirkilionis

Sbano²

2010

Advs. Complex Syst.

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Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a central bottleneck problem in many application areas, especially in cell biology where various such diagrams with different conventions describing molecular regulation are presently in use. In most situations these diagrams can only be interpreted by the use of both discrete and continuous variables during the modelling process, corresponding to both deterministic and stochastic hybrid dynamics. The conventions in genetics are well-known, and therefore we use this field for illustration purposes. In [25] and [26] the authors showed that with the help of a multi-scale analysis stochastic systems with both continuous variables and finite state spaces can be approximated by dynamical systems whose leading order time evolution is given by a combination of ordinary differential equations (ODEs) and Markov chains. The leading order term in these dynamical systems is called average dynamics and turns out to be an adequate concept to analyse a class of simplified hybrid systems. Once the dynamics is defined the mutual interaction of both ODEs and Markov chains can be analysed through the (reverse) introduction of the so called Interaction Graph, a concept originally invented for time-continuous dynamical systems, see [5]. Here we transfer this graph concept to the average dynamics, which itself is introduced as an heuristic tool to construct models of reaction or contact networks. The graphical concepts introduced form the basis for any subsequent study of the qualitative properties of hybrid models in terms of connectivity and (feedback) loop formation. arXiv:0803.0635v3 [q-bio.MN]

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Section: Introductionmentioning

confidence: 82%

An Averaging Principle for Combined Interaction Graphs — Connectivity and Applications to Genetic Switches

Kirkilionis

Sbano²

2010

Advs. Complex Syst.

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“…On the basis of the two-inputs two-outputs interactive process model considered in this paper, predictive controllers are realized using generalized predictive control (GPC) design methodology to maintain tight control in the presence of interactions. The general predictive control (GPC) method, proposed in ref , has become one of the most popular model predictive control methods used in the industry. Various model predictive control algorithms can be found in refs − .…”

Section: Introductionmentioning

confidence: 99%

Predictive Ratio Control for Interacting Processes

Tan

Tay

Zhao

et al. 2009

Ind. Eng. Chem. Res.

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In this paper, a predictive-PID ratio control scheme is developed for multivariable processes. The Generalized predictive control based PID configuration is incorporated into various conventional ratio control schemes. Conventional parallel and series ratio control cannot satisfy the stringent requirements. The proposed method is applied to the wafer temperature uniformity control in the lithography. Both simulation and experimental results show the effectiveness of the proposed predictive ratio control method.

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Multi-scale genetic dynamic modelling II: application to synthetic biology

Kirkilionis

Janus

Sbano³

2011

Theory Biosci.

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We model in detail a simple synthetic genetic clock that was engineered in Atkinson et al. (Cell 113(5):597-607, 2003) using Escherichia coli as a host organism. Based on this engineered clock its theoretical description uses the modelling framework presented in Kirkilionis et al. (Theory Biosci. doi: 10.1007/s12064-011-0125-0 , 2011, this volume). The main goal of this accompanying article was to illustrate that parts of the modelling process can be algorithmically automatised once the model framework we called 'average dynamics' is accepted (Sbano and Kirkilionis, WMI Preprint 7/2007, 2008c; Kirkilionis and Sbano, Adv Complex Syst 13(3):293-326, 2010). The advantage of the 'average dynamics' framework is that system components (especially in genetics) can be easier represented in the model. In particular, if once discovered and characterised, specific molecular players together with their function can be incorporated. This means that, for example, the 'gene' concept becomes more clear, for example, in the way the genetic component would react under different regulatory conditions. Using the framework it has become a realistic aim to link mathematical modelling to novel tools of bioinformatics in the future, at least if the number of regulatory units can be estimated. This should hold in any case in synthetic environments due to the fact that the different synthetic genetic components are simply known (Elowitz and Leibler, Nature 403(6767):335-338, 2000; Gardner et al., Nature 403(6767):339-342, 2000; Hasty et al., Nature 420(6912):224-230, 2002). The paper illustrates therefore as a necessary first step how a detailed modelling of molecular interactions with known molecular components leads to a dynamic mathematical model that can be compared to experimental results on various levels or scales. The different genetic modules or components are represented in different detail by model variants. We explain how the framework can be used for investigating other more complex genetic systems in terms of regulation and feedback.

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Hybrid model predictive control of induction of Escherichia coli

Cited by 3 publications

References 23 publications

An Averaging Principle for Combined Interaction Graphs — Connectivity and Applications to Genetic Switches

An Averaging Principle for Combined Interaction Graphs — Connectivity and Applications to Genetic Switches

Predictive Ratio Control for Interacting Processes

Multi-scale genetic dynamic modelling II: application to synthetic biology

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