Integral control for population management

Guiver, Chris; Logemann, Hartmut; Rebarber, Richard; Bill, Adam; Tenhumberg, Brigitte; Hodgson, David J.; Townley, Stuart

doi:10.1007/s00285-014-0789-4

Cited by 11 publications

(26 citation statements)

References 87 publications

(81 reference statements)

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“…Regarding the mean dynamics, we can see that increasing K p and, hence, β, to reasonable levels improves the settling-time as depicted in Figure 11 for the special case of k = 3. However, this is far from being the general case since the settling-time can exhibit a quite complex behavior for this network (see 14). The stationary variance depicted in Figure 13 exhibits here a rather standard and predictive behavior where a small k and a large K p both lead to its reduction.…”

Section: Example -Gene Expression Network With Protein Maturationmentioning

confidence: 91%

“…Note that this controller can still be employed for the in-silico control of single-cells using a stochastic controller as, in this case, we would not be restricted anymore to mass-action, Hill or Michaelis-Menten kinetics. This was notably considered in the case of in-silico population control in [7,8,14]. The second type of negative feedback action, referred to as the Hill feedback, consists of the reaction (8) but involves the non-cooperative repressing Hill function F (X ) = K p /(1 + X ) as propensity function.…”

Section: Negative Feedback Actionmentioning

confidence: 99%

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Variance reduction for antithetic integral control of stochastic reaction networks

Briat

Gupta

Khammash

2017

Preprint

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The antithetic integral feedback motif recently introduced in [6] is known to ensure robust perfect adaptation for the mean dynamics of a given molecular species involved in a complex stochastic biomolecular reaction network. However, it was observed that it also leads to a higher variance in the controlled network than that obtained when using a constitutive (i.e. open-loop) control strategy. This was interpreted as the cost of the adaptation property and may be viewed as a performance deterioration for the overall controlled network. To decrease this variance and improve the performance, we propose to combine the antithetic integral feedback motif with a negative feedback strategy. Both theoretical and numerical results are obtained. The theoretical ones are based on a tailored moment closure method allowing one to obtain approximate expressions for the stationary variance for the controlled network and predict that the variance can indeed be decreased by increasing the strength of the negative feedback. Numerical results verify the accuracy of this approximation and show that the controlled species variance can indeed be decreased, sometimes below its constitutive level. Three molecular networks are considered in order to verify the wide applicability of two types of negative feedback strategies. The main conclusion is that there is a trade-off between the speed of the settling-time of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is associated with larger settling-time. Author summaryHomeostasis, the ability of living organisms to regulate their internal state, is of fundamental importance for their adaptation to environmental changes and their survival. This is the reason why complex regulatory genetic networks evolved and allowed for the emergence of more and more complex organisms. Recently, the theoretical study of those regulatory networks using ideas and concepts from control theory and the design of novel ones have gained a lot of attention. Synthetic regulatory circuits are seen as elementary building blocks for the design of complex networks that need to incorporate some regulating elements to be fully functional. This is for instance the case in metabolic engineering where the production of biomolecules, such as drugs or biofuels, need to be optimized and tightly regulated. A particular circuit, the so-called antithetic integral controller, is now known to ensure homeostasis even when regulatory circuits are subject to randomness. However, it is also known that this circuit increases variability in the network. The effects of a correcting negative feedback loop on the variance are discussed here and it is shown that variability can be reduced this way. Notably, we show that there is a tradeoff between speed of the network and variability.

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Section: Example -Gene Expression Network With Protein Maturationmentioning

confidence: 91%

Section: Negative Feedback Actionmentioning

confidence: 99%

Variance reduction for antithetic integral control of stochastic reaction networks

Briat

Gupta

Khammash

2017

Preprint

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“…In practical applications, however, the conservatism of adaptive control schemes must be traded off against the economic and social costs of not sufficiently reducing pest abundance-a possible consequence of a supposed optimal management strategy not functioning as intended owing to a lack of robustness, say to model uncertainty. As we have argued elsewhere [64], when seeking to control uncertain population models, open-loop control strategies, that is, those based on (estimated) model parameters and not on measured variables, may not achieve the control objective, whereas robust feedback controls do. The same is true of certain optimal control strategies; see [64] and the references therein.…”

Section: Discussionmentioning

confidence: 99%

“…As we have argued elsewhere [64], when seeking to control uncertain population models, open-loop control strategies, that is, those based on (estimated) model parameters and not on measured variables, may not achieve the control objective, whereas robust feedback controls do. The same is true of certain optimal control strategies; see [64] and the references therein.…”

Section: Discussionmentioning

confidence: 99%

Simple Adaptive Control for Positive Linear Systems with Applications to Pest Management

Guiver¹,

Edholm²,

Jin³

et al. 2016

SIAM J. Appl. Math.

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Abstract. Pest management is vitally important for modern arable farming, but models for pest species are often highly uncertain. In the context of pest management, control actions are naturally described by a nonlinear feedback that is generally unknown, which thus motivates a robust control approach. We argue that adaptive approaches are well suited for the management of pests and propose a simple high-gain adaptive tuning mechanism so that the nonlinear feedback achieves exponential stabilization. Furthermore, a switched adaptive controller is proposed, cycling through a set of given control actions, that also achieves global asymptotic stability. Such a model in practice allows for the possibility of rotating between different courses of management action. In developing our control strategies we appeal to comparison and monotonicity arguments. Interestingly, componentwise nonnegativity of the model, combined with an irreducibility assumption, implies that several issues typically associated with high-gain adaptive controllers do not arise and usual high-gain structural assumptions are not required.

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“…This problem and its variations have been addressed in the past using various approaches. A thoroughly considered approach relies on the use of an ON-OFF nonlinearity placed between the controller and the system; [9,10,12,29]. The main issue is that an ON-OFF integrator cannot be readily implemented in terms of chemical reactions and, hence, cannot be implemented inside biological organisms.…”

Section: The Control Problem and The Antithetic Integral Controllermentioning

confidence: 99%

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

Briat¹

2020

SIAM J. Appl. Dyn. Syst.

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The integral control of positive systems using nonnegative control input is an important problem arising, among others, in biochemistry, epidemiology and ecology. An immediate solution is to use an ON-OFF nonlinearity between the controller and the system. However, this solution is only available when controllers are implemented in computer systems. When this is not the case, like in biology, alternative approaches need to be explored. Based on recent research in the control of biological systems [7,14], we propose to develop a theory for the integral control of positive systems using nonnegative controls based on the so-called antithetic integral controller and two positively regularized integral controllers, the so-called exponential integral controller and logistic integral controller. For all these controllers, we establish several qualitative results, which we connect to standard results on integral control. We also obtain additional results which are specific to the type of controllers. For instance, we show an interesting result stipulating that if the gain of the antithetic integral controller is suitably chosen, then the local stability of the equilibrium point of the closed-loop system does not depend on the choice for the coupling parameter, an additional parameter specific to this controller. Conversely, we also show that if the coupling parameter is suitably chosen, then the equilibrium point of the closed-loop system is locally stable regardless the value of the gain. For the exponential integral controller, we can show that the local stability of the equilibrium point of the closed-loop system is independent of the gain of the controller and the gain of the system. The stability only depends on the exponential rate of the controller, again a parameter that is specific to this type of controllers. Several examples are given for illustration.

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Integral control for population management

Cited by 11 publications

References 87 publications

Variance reduction for antithetic integral control of stochastic reaction networks

Variance reduction for antithetic integral control of stochastic reaction networks

Simple Adaptive Control for Positive Linear Systems with Applications to Pest Management

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

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