Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems

Lakshmi Narayan Sridhar

doi:doi:10.11648/j.ijssam.20240903.11

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Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems

Lakshmi Narayan Sridhar^*

Published in International Journal of Systems Science and Applied Mathematics (Volume 9, Issue 3)

Received: 1 October 2024 Accepted: 17 October 2024 Published: 11 November 2024

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Abstract

Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 9, Issue 3)
DOI	10.11648/j.ijssam.20240903.11
Page(s)	37-43
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ecosystem, Bifurcation, Optimal Control

References

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APA Style

Sridhar, L. N. (2024). Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. International Journal of Systems Science and Applied Mathematics, 9(3), 37-43. https://doi.org/10.11648/j.ijssam.20240903.11

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ACS Style

Sridhar, L. N. Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. Int. J. Syst. Sci. Appl. Math. 2024, 9(3), 37-43. doi: 10.11648/j.ijssam.20240903.11

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AMA Style

Sridhar LN. Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. Int J Syst Sci Appl Math. 2024;9(3):37-43. doi: 10.11648/j.ijssam.20240903.11

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@article{10.11648/j.ijssam.20240903.11,
  author = {Lakshmi Narayan Sridhar},
  title = {Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems
},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {9},
  number = {3},
  pages = {37-43},
  doi = {10.11648/j.ijssam.20240903.11},
  url = {https://doi.org/10.11648/j.ijssam.20240903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20240903.11},
  abstract = {Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.
},
 year = {2024}
}

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TY  - JOUR
T1  - Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems

AU  - Lakshmi Narayan Sridhar
Y1  - 2024/11/11
PY  - 2024
N1  - https://doi.org/10.11648/j.ijssam.20240903.11
DO  - 10.11648/j.ijssam.20240903.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 37
EP  - 43
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20240903.11
AB  - Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.

VL  - 9
IS  - 3
ER  -

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Author Information

Lakshmi Narayan Sridhar

Department of Chemical Engineering, University of Puerto Rico, Mayaguez, Puerto Rico

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APA Style

Sridhar, L. N. (2024). Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. International Journal of Systems Science and Applied Mathematics, 9(3), 37-43. https://doi.org/10.11648/j.ijssam.20240903.11

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ACS Style

Sridhar, L. N. Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. Int. J. Syst. Sci. Appl. Math. 2024, 9(3), 37-43. doi: 10.11648/j.ijssam.20240903.11

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AMA Style

Sridhar LN. Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems. Int J Syst Sci Appl Math. 2024;9(3):37-43. doi: 10.11648/j.ijssam.20240903.11

Copy | Download

@article{10.11648/j.ijssam.20240903.11,
  author = {Lakshmi Narayan Sridhar},
  title = {Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems
},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {9},
  number = {3},
  pages = {37-43},
  doi = {10.11648/j.ijssam.20240903.11},
  url = {https://doi.org/10.11648/j.ijssam.20240903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20240903.11},
  abstract = {Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems

AU  - Lakshmi Narayan Sridhar
Y1  - 2024/11/11
PY  - 2024
N1  - https://doi.org/10.11648/j.ijssam.20240903.11
DO  - 10.11648/j.ijssam.20240903.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 37
EP  - 43
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20240903.11
AB  - Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.

VL  - 9
IS  - 3
ER  -

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