An Optimal Control Study with Quantity of Additional food as Control in Prey-Predator Systems involving Inhibitory Effect

Ananth, V.S.; Vamsi, D. K. K.

doi:10.1515/cmb-2020-0121

Cited by 4 publications

(1 citation statement)

References 45 publications

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“…The multivariable Lotka-Volterra model has been primarily conceived to describe the interaction of competing populations (Ye et al, 2022), (Massaroli et al, 2020), (Zhang et al, 2015), (Tiao et al, 2021). It has found ample use in biology, ecology, agricultural production management or even in economics (Chakraborty et al, 2011), (Becker and Leopoldo-Wildburger, 2020), (Aranth and Vomsi, 2021). The model is also known as the prey-predator system, and its state variables represent the population of prey and predator species (Babaci and Shafiee, 2019), (Li et al, 2018), (Qian et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Rigatos,

Wira,

Siano

et al. 2024

Preprint

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The multivariable Lokta-Volterra dynamic model has been widely used to describe interacting and competing populations and has found applications in biology, ecology, agricultural production management and in economics. In this article a nonlinear optimal (H-infinity) control method is developed for the Lotka-Volterra system. First, differential flatness properties are proven for the associated state-space model. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

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Section: Introductionmentioning

confidence: 99%

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Rigatos,

Wira,

Siano

et al. 2024

Preprint

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Achieving Minimum-Time Biological Conservation and Pest Management for Additional Food provided Predator–Prey Systems involving Inhibitory Effect: A Qualitative Investigation

Ananth

Vamsi

2021

Acta Biotheor

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Theoretical and experimental studies on prey-predator systems where predator is supplied with alternate sources of food have received significant attention over the years due to their relevance in achieving biological conservation and biological control. Some of the outcomes of these studies suggest that with appropriate quality and quantity of additional food, the system can be steered towards any desired state eventually with time. One of the limitations of previous studies is that the desired state is reached asymptotically, which makes the outcomes not easily applicable in practical scenarios. To overcome this limitation, in this work, we formulate and study optimal control problems to achieve the desired outcomes in minimum (finite) time.We consider two different models of additional food provided prey-predator systems involving Holling type IV functional response (with inhibitory effect of prey). In the first scenario, additional food is incorporated implicitly into the predator's functional response with a possibility of achieving biological conservation through co-existence of species and biological control by maintaining prey at a level that is least harmful to the system. In the second, the effect of additional food is incorporated explicitly into the predator's compartment with the goal of pest management by maintaining prey density at a very minimal damaging level. For both cases, appropriate optimal control strategies are derived and the theoretical findings are illustrated by numerical simulations. We also discuss the ecological significance of the theoretical findings for both models.

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Stochastic optimal and time-optimal control studies for additional food provided prey–predator systems involving Holling type III functional response

Prakash

Vamsi

2023

Computational and Mathematical Biophysics

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This article consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modelled as an additional food-provided prey–predator system with Holling type III functional response for predator and intra-specific competition among predators. We first discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Second, we consider an optimal control problem in the time-optimal control setting. We initially establish the existence of optimal controls for both these problems and later characterize these optimal controls using the Stochastic maximum principle. Further numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.

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An Optimal Control Study with Quantity of Additional food as Control in Prey-Predator Systems involving Inhibitory Effect

Cited by 4 publications

References 45 publications

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Achieving Minimum-Time Biological Conservation and Pest Management for Additional Food provided Predator–Prey Systems involving Inhibitory Effect: A Qualitative Investigation

Stochastic optimal and time-optimal control studies for additional food provided prey–predator systems involving Holling type III functional response

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