CONTROL AND IDENTIFICATION OF CONTROLLED AUTO-REGRESSIVE MOVING AVERAGE (CARMA) FORM OF AN INTRODUCED SINGLE-INPUT SINGLE-OUTPUT TUMOR MODEL
DOI:
https://doi.org/10.29121/ijetmr.v11.i2.2024.1403Keywords:
Gradient Based Iterative Algorithms, 2-Stage Identification, System Identification, Parameter Estimation, Tumor ModelAbstract
The article investigates the parameter estimation for controlled auto-regressive moving average models with gradient based iterative approach and two-stage gradient based iterative approach. Since deriving a new model for tumor model is substantial, introduced system identification algorithms are used in order to estimate parameters of a specific nonlinear tumor model. Besides, in order to estimate tumor model a collection of output and input data is taken from the nonlinear system. Apart from that, effectiveness of the identification algorithms such as convergence rate and estimation error is depicted through various tables and figures. Finally, it is shown that the two stage approach has higher identification efficacy.
Downloads
References
Bin, X. I. (2012). A Two-Stage ARMAX Identification Approach Based on Bias-Eliminated Least Squares and Parameter Relationship Between MA Process and Its Inverse. Acta Automática Sinica, 491-496. https://doi.org/10.1016/S1874-1029(11)60310-8
Bobál, V. E. (2006). Digital Self-Tuning Controllers: Algorithms, Implementation and Applications. Springer Science & Business Media.
Chen, H.-F., & Guo, L. (1987). Optimal Adaptive Control and Consistent Parameter Estimates for ARMAX Model with Quadratic Cost. SIAM Journal on Control and Optimization, 845-867. https://doi.org/10.1137/0325047
Chen, J. Q. (2020). Modified Kalman Filtering Based Multi-Step-Length Gradient Iterative Algorithm for ARX Models with Random Missing Outputs. Automatica. https://doi.org/10.1016/j.automatica.2020.109034
De Pillis, L. G. (2001). A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach. Computational and Mathematical Methods in Medicine, 79-100. https://doi.org/10.1080/10273660108833067
Ding, F. A. (2005). Gradient Based Iterative Algorithms for Solving a Class of Matrix Equations. IEEE Transactions on Automatic Control, 1216-1221. https://doi.org/10.1109/TAC.2005.852558
Ding, F. E. (2019). Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data. Mathematics. https://doi.org/10.3390/math7050428
Ding, F. E. (2020). Gradient Estimation Algorithms for the Parameter Identification of Bilinear Systems using the Auxiliary Model. Journal of Computational and Applied Mathematics. https://doi.org/10.1016/j.cam.2019.112575
Ding, F. E. (2020). Two-Stage Gradient-Based Iterative Estimation Methods for Controlled Autoregressive Systems using the Measurement Data. International Journal of Control, Automation and Systems, 886-896. https://doi.org/10.1007/s12555-019-0140-3
Ding, F. E. (2018). Iterative Parameter Identification for Pseudo-Linear Systems with ARMA Noise Using the Filtering Technique. IET Control Theory and Applications. https://doi.org/10.1049/iet-cta.2017.0821
Du, D. E. (2017). A Novel Networked Online Recursive Identification Method for Multivariable Systems with Incomplete Measurement Information. IEEE Transactions on Signal and Information Processing over Networks, 744-759. https://doi.org/10.1109/TSIPN.2017.2662621
Ji, Z. E. (2020). An Attention-Driven Two-Stage Clustering Method for Unsupervised Person Re-Identification. Computer Vision-ECCV 2020: 16th European Conference. https://doi.org/10.1007/978-3-030-58604-1_2
Lee, J. K. (1994). A Two-Stage Neural Network Approach for ARMA Model Identification with ESACF. Decision Support Systems. https://doi.org/10.1016/0167-9236(94)90019-1
Li, K., Peng, J.-X., & Bai, E.-W. (2006). A Two-Stage Algorithm for Identification of Nonlinear Dynamic Systems. Automatica, 1189-1197. https://doi.org/10.1016/j.automatica.2006.03.004
Li, L. Z. (2020). A Two-Stage Maximum a Posterior Probability Method for Blind Identification of LDPC Codes. IEEE Signal Processing Letters, 111-115. https://doi.org/10.1109/LSP.2020.3047334
Li, M. A (2018). The Least Squares Based Iterative Algorithms for Parameter Estimation of a Bilinear System with Autoregressive Noise Using the Data Filtering Technique. Signal Processing, 23-34. https://doi.org/10.1016/j.sigpro.2018.01.012
Li, M. A. (2018). Auxiliary Model Based Least Squares Iterative Algorithms for Parameter Estimation of Bilinear Systems using Interval-Varying Measurements. IEEE Access, 21518-21529. https://doi.org/10.1109/ACCESS.2018.2794396
Li, M. A. (2020). Maximum Likelihood Least Squares Based Iterative Estimation for a Class of Bilinear Systems using the Data Filtering Technique. International Journal of Control, Automation and Systems, 1581-1592. https://doi.org/10.1007/s12555-019-0191-5
Li, M. A. (2021). Maximum Likelihood Hierarchical Least Squares-Based Iterative Identification for Dual-Rate Stochastic Systems. International Journal of Adaptive Control and Signal Processing, 240-261. https://doi.org/10.1002/acs.3203
Liu, Y. D. (2010). Least Squares Based Iterative Algorithms for Identifying Box-Jenkins Models with Finite Measurement Data. 1458-1467. https://doi.org/10.1016/j.dsp.2010.01.004
Lobato, F. S. (2016). Determination of an Optimal Control Strategy for Drug Administration in Tumor Treatment using Multi-Objective Optimization Differential Evolution. Computer Methods and Programs in Biomedicine, 51-61. https://doi.org/10.1016/j.cmpb.2016.04.004
Ma, H. E. (2020). Partially-Coupled Gradient-Based Iterative Algorithms for Multivariable Output-Error-Like Systems with Autoregressive Moving Average Noises. IET Control Theory and Applications, 2613-2627. https://doi.org/10.1049/iet-cta.2019.1027
Osorio-Arteaga, F. J.-D. (2020). Robust Multivariable Adaptive Control of Time-Varying Systems. IAENG International Journal of Computer Science, 605-612.
Raja, M. A. (2015). Two-Stage Fractional Least Mean Square Identification Algorithm for Parameter Estimation of CARMA Systems. Signal Processing, 327-339. https://doi.org/10.1016/j.sigpro.2014.06.015
Sadeghi, K. H. (2023). Efficient Identification Algorithm for Controlling Multivariable Tumor Models: Gradient-Based and Two-Stage Method. Advanced Mathematical Models and Applications, 8(2), 185-198.
Sadeghi, K. H. (2023). Multi-Innovation Iterative Identification Algorithms for CARMA Tumor Models. International Review on Modelling and Simulation. https://doi.org/10.15866/iremos.v16i2.23270
Sadeghi, K. H. (2023). Utilizing ARMA Models for System Identification in Stirred Tank Heater: Different Approaches. Computing Open. https://doi.org/10.1142/S2972370123300030
Sweilam, N. H., & AL-Mekhlafi, S. M. (2018). Optimal Control for a Nonlinear Mathematical Model of Tumor Under Immune Suppression: A Numerical Approach. Optimal Control Applications and Methods, 1581-1596. https://doi.org/10.1002/oca.2427
Wang, L. E. (2020). Decomposition-Based Multiinnovation Gradient Identification Algorithms for a Special Bilinear System Based on its Input-Output Representation. International Journal of Robust and Nonlinear Control, 3607-3623. https://doi.org/10.1002/rnc.4959
Wang, M. X. (2007). "Iterative Algorithms for Solving the Matrix Equation AXB+ CXTD= E.". Applied Mathematics and Computation, 622-629.
Watanabe, K. T. (1992). An Adaptive Control for CARMA Systems Using Linear Neural Networks. International Journal of Control, 483-497. https://doi.org/10.1080/00207179208934324
Wei, Z. E. (2017). Online Model Identification and State-of-Charge Estimate for Lithium-Ion Battery with a Recursive Total Least Squares-Based Observer. IEEE Transactions on Industrial Electronics, 1336-1346.
Xie, L. Y. (2010). Gradient Based and Least Squares Based Iterative Algorithms for Matrix Equations AXB+ CXTD= F. Applied Mathematics and Computation, 2191-2199. https://doi.org/10.1016/j.amc.2010.07.019
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Kiavash Hossein Sadeghi, Abolhassan Razminia, Abolfaz Simorgh
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere.
- That its release has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with International Journal of Engineering Technologies and Management Research agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
For More info, please visit CopyRight Section
