RADIAL BASIS NEURAL NETWORK FOR THE SOLUTION OF OPTIMAL CONTROL PROBLEMS VIA SIMULINK
Main Article Content
Abstract
This study uses radial basis neural network to solve optimum control problems via simulink. Using Pontryaginí's principle, the optimal control problem's optimum system is constructed. MATLAB is used to simulate the optimality system and generate the simulink architecture for the trial value. A radial basis neural network is then used to train the system and produce the optimal solution. This approach's effectiveness is evaluated using a few control problems, and it is shown to be effective because of the reliable, accurate, and consistent results that are produced. The performance of this strategy is superior to that of other approaches.
Downloads
Metrics
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
References
R. R. Garret, Numerical Methods for Solving Optimal Control Problems,Tennessee Research and Creative Exchange, University of Tennessee, Knoxville (2015). http:/trace.tennessee.edu/utk-gradthes/3401.
A. K. Johan, P. Joos, L. R. D. Bart, Artficial Neural Networks for Modelling and control of Non-Linear systems, Springer Science+Business MediaDordrecht (1996) 83-88.
S. Adamu, O. O. Aduroja, K. Bitrus, Numerical Solution to Optimal Control Problems using Collocation Method via Pontrygin's Principle, FUDMA Journal of Sciences 7(5) (2023) 228-233. DOI: https://doi.org/10.33003/fjs-2023-0705-2016.
O. O. Aduroja, S. Adamu, M. Kida & H. L. Buhari (2024). Bi-Basis Function Second Derivative Block Method for the Solution of Optimal Control Problems. International Journal of Development Mathematics 1(1) 16 - 24. https://doi.org/10.62054/ijdm/0101.02.
S. Adamu, Numerical Solution of Optimal Control Problems using Block Method, Electronic Journal of Mathematical Analysis and Applications 11(2) (2023) 1-12. http://ejmaa.journals.ekb.eg/.
R. E. Bellman, The theory of dynamic programming, Bull. Amer.Math. Soc. 60(6) (1954) 503--515.
S. Adamu, S., Aduroja, O. O., Onanaye, A. S. & Odekunle, M. R. (2024). Iterative method for the numerical solution of optimal control model for mosquito and insecticide. J. Nig. Soc. Phys. Sci. 6(2024) 1965. DOI: https://doi.org/10.46481/jnsps.2024.1965.
M. T. Hagan, H. B. Demuth, M. H. Beak, Neural network design, pws publishing, Boston (1996).
S. Lenhart, J. T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall/CRC, Boca Raton (2007).
S. Adamu, A. M. Alkali & M. R. Odekunle (2024). Runge-Kutta Like Method for the Solution of Optimal Control Model of Real Investment and Fish Management. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 15(2), 155-169.
DOI: https://doi.org/10.61841/turcomat.v15i2.14646.
W. Zhang, Computational ecology. Artificial neural network and their applications, World Scientific Publishing Co. pte. Ltd (2014).
O. Awodele, O. Jegede, Neural network and its application in engineering, Proceedings of informing science & IT education conference (2009). doi:10.28945/3317.
W. E. Boyce, R. C. Diprima, Elementary differential equations and boundary value problems, John Wiley & sons, inc. Newyork (2011).
A. Danney, A Software Safety Certification Plug-in for Automated Code Generators: Feasibility Study and Preliminary Design, NASA Ames Research Center, Muffet Field, CA 94035 (2011).
M. J. D. Powell, Radial Basis Functions for Multivariable Interpolation: A Review (1987).
D. S. Broom, D. Lowe, Radial basis functions, multi-variable functional interpolation and adaptive networks (No. RSRE-MEMO-4148), Royal Signals and Radar Establishment Malvern, United Kingdom (1988).
H. Yu, T. Xie, S. Paszczynski, B. M. Wilamowski, Advantages of radial basis function networks for dynamic system design, IEEE Transactions on Industrial Electronics 58 (12) (2011) 5438 - 5450.
R. L. Gyo, M. Kohler, A. Krzyzak, H. Walk, A Distribution Free Theory of Non-Parametric Regression, Springer Verlag, New York Inc (2002).
S. Effati, M. Pakdaman, Optimal control problem via neural networks, Neural Computer and Application (2017). doi:10.1007/s00521-012-1156-2.
M. T. Hagan, H. B. Demuth, M. H. Beak, Neural network design, pws publishing, Boston (1996).
N. A. Khan, A. Shaikh, F. Sultan, A. Ara, Numerical simulaion using artificial neural network on fractional differential equations, Numerical simulation-From Brain imaging to Turbulent Flow (2016) 98-112. Doi:10.5772/64151.
Y. H. Pao, M. Philips, D. J. Sobajic, Neural-net computing and the intelligent control of systems, International Journal of control 56(2) (1992) 263-289. Doi.org/10.1080/00207179208934315.
L. Gongi, C. Liu, Y. Li & F. Yuan, Training Feed-forward Neural Networks Using the Gradient Descent Method with the Optimal Stepsize. Journal of Computational Information Systems 8(4) (2012) 1359{1371 http://www.Jofcis.com
X. Zhou, W. Zhang, Z. Chen, S. Diao & T. Zhangy, Efficient Neural Network Training via Forward and Backward Propagation Sparsification. 35th Conference on Neural Information Processing Systems (NeurIPS 2021), Sydney, Australia.
A. Kohan, E. A. Rietman & H. T. Siegelmann, Forward Signal Propagation Learning. IEEE Transactions on Neural Networks and Learning (2022).
B. Yin, F. Corradi & S. M. Bohté, Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time. Nature Machine Intelligence, 5(May) (2023) 518--527. https://doi.org/10.1038/s42256-023-00650-4.
Y. Neha, Y. Anupam, K. Manoj, An Introduction to Neural Network Methods for Differential Equations, New York. Springer Dordrecht Heidelberg (2015) 24 -- 30.
K. L. Du, M. N. S. Swamy, Radial Basis Function Networks, Neural Networks in a Softcomputing Framework, Springer, London (2006) 251 - 294.