Mathematical modeling and control of population systems: Applications in biological pest control

The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction.Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system.

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“…Theorem 4.1 (Rafikov et al 2008) If there exist matrices P , Q, R ∈ R n×n ; P positive definite and Q symmetric, such that the function…”

Section: Linear Feedback Control For the Radiationmentioning

confidence: 99%

Observation and control in a model of a cell population affected by radiation

et al. 2009

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“…In the paper a control-theoretic methodology has been proposed for a particular tasks open-loop equilibrium control, the novelty of our paper is that for the considered trophic 7 chain, an efficient method for the calculation of the equilibrium control is proposed, by 8 setting up and solving an optimal control problem. can be also applied to find a closed-loop equilibrium control of a non-Lotka-Volterra 13 type trophic chain into a new equilibrium, realizing a controlled regime shift.…”

mentioning

confidence: 99%

“…Finally, in the Appendix we recall some basic concepts and results applied in the 7 present paper. 8 2. Description of the dynamic model 9 For the presentation of our approach we consider a relatively simple food web, a 10 trophic chain involving a resource, a plant and a herbivorous animal.…”

mentioning

confidence: 99%

“…This, in 5 dynamic situation, i.e. in case of a long-term human intervention, typically requires the 6 approach of mathematical systems theory (in frequently used terms, state-space 7 modelling), see Kalman et al (1969) for the basic results of this theory, and Chen et al 8 (2004) for a recent reference. This methodology offers solutions not only to controlling 9 but also to monitoring (i.e.…”

mentioning

confidence: 99%

“…From the local controllability of the control system (3.4), we know 6 that the optimal control problem (3.5)-(3.7) has at least one solution. 7 As a consequence of this theorem, for an effective calculation of an equilibrium 8 control u , it is enough to solve the optimal control problem (3.5)-(3.7). We note that, since by Remark 2.2, for the uncontrolled system,  x is asymptotically 3 stable, the state would tend to  x , reaching it in "infinite time", as seen in Figure 2.c.…”

mentioning

confidence: 99%

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Open- and closed-loop equilibrium control of trophic chains

Gámez

López

Shamandy

2010

Ecological Modelling

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Tensor product model transformation‐based control for fractional‐order biological pest control systems

Boonyaprapasorn

Kuntanapreeda

Ngiamsunthorn

et al. 2020

Asian Journal of Control

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As environmental pollution and safety of human and creatures have been an issue of concern, pest management based on nonchemical use is preferable. Biological pest control can satisfy the regulation of pest population without causing environmental problems. Moreover, representation of dynamical systems in the form of fractional‐order dynamic models can explain several phenomena better than the integer‐order dynamic models can. The aim of this study is to determine the biological pest control policy for the fractional‐order pest control systems, which is a complex nonlinear multiple input and multiple output control problem. Here, the system is represented in the form of a fractional‐order Lotka–Volterra model. In order to avoid complexity in the nonlinear feedback controller design process, the tensor product (TP) model transformation was applied to automatically transform the biological pest control system to the TP polytopic model which allows the designer to synthesize the controller under linear framework. Moreover, the design process can be easily carried out by solving an linear matrix inequality (LMI) problem, which is very well applicable to high‐dimensional multiple input and multiple output control problems. Simulation studies were conducted to demonstrate the ease of the TP‐based design process. The simulation results showed that the designed control policy effectively manipulates the pest populations of the fractional‐order Lotka–Volterra model to the desired level which is economically viable.

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Mathematical modeling and control of population systems: Applications in biological pest control

Cited by 71 publications

References 11 publications

Observation and control in a model of a cell population affected by radiation

Observation and control in a model of a cell population affected by radiation

Open- and closed-loop equilibrium control of trophic chains

Tensor product model transformation‐based control for fractional‐order biological pest control systems

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