کنترل مد لغزشی مبتنی بر داده مبتنی بر شبکه عصبی بازگشتیتصویر برای عفونت :HIV یک رویکرد مقدار تکین
محورهای موضوعی : مهندسی برق و کامپیوتراشکان ضرغامی 1 , مهدی سیاهی 2 , فریدون نوشیروان راحت آباد 3
1 - دانشكده مهندسي برق، دانشگاه آزاد اسلامی واحد تهران مرکز
2 - دانشکده مهندسي برق و کامپیوتر، دانشگاه آزاد اسلامی واحد علوم و تحقیقات
3 - دانشکده مهندسی پزشکی، دانشگاه آزاد اسلامی واحد علوم و تحقیقات
کلید واژه: کنترل مد لغزشی مبتنی بر داده, شبکه عصبی بازگشتی تصویر, رویکرد مقدار تکین, عفونت HIV,
چکیده مقاله :
در این مقاله، جبران‌سازی عفونت HIV با استفاده از کنترل مد لغزشی مبتنی بر داده در تلفیق با شبکه عصبی بازگشتی تصویر مورد توجه قرار گرفته است. اهداف اصلی تعیین قوانین کنترلی به‌گونه‌ای است که نیازی به معادلات ریاضی عفونت HIV نباشد و محدودیت فیزیکی محرک نیز برآورده شود. این کار با توسعه مبانی کنترل تطبیقی مستقل از مدل صورت می‌گیرد که در آن از خطی‌سازی دینامیکی محلی مبتنی بر تخمین مشتق شبه‌جزئی برای توصیف رابطه بین ورودی و خروجی استفاده می‌شود. برای تعیین قانون کنترل، نخست یک شاخص عملکرد مبتنی بر تحقق شرط دسترسی نمایی زمان گسسته تعریف می‌شود. با تبدیل این شاخص به یک مسئله برنامه‌ریزی مرتبه دوی مقید، دینامیک شبکه عصبی بازگشتی تصویر بر اساس نظریه تصویر استخراج می‌شود. به کمک معادله خروجی بهینه‌سازی، دینامیک حلقه بسته به‌صورت صریح تعیین می‌گردد و تحلیل پایداری حلقه بسته به کمک رویکرد مقدار تکین مورد بررسی قرار می‌گیرد. نتایج شبیه‌سازی الگوریتم پیشنهادی در قیاس با یکی از جدیدترین رویکردهای کنترلی، نشان‌دهنده کیفیت بالای الگوریتم در هدایت دینامیک عفونت HIV به نقطه تعادل سالم در حضور عدم قطعیت مدل و اغتشاشات خارجی است.
In the present study, drug treatment of HIV infection is investigated using a Data-Driven Sliding Mode Control (DDSMC) combined with a Projection Recurrent Neural Network (PRNN). The major objective is to establish the control law that eliminates the need for HIV infection mathematical formulae and ensures that the physical limits of the actuator are reached. This is accomplished by creating the concepts of model-free adaptive control, in which the relation between input and output is described using local dynamic linearized models based on quasi-partial derivatives. To determine the DDSMC law, a performance index is first defined based on the fulfillment of a discrete-time exponential reaching condition. By turning this index into a quadratic programming problem, the dynamics of the PRNN are extracted based on projection theory. The closed-loop system is explicitly determined using the optimizer output equation and the closed-loop stability analysis is evaluated using the singular value approach. The simulation results reveal that the proposed algorithm has robust performance in conducting the state variables of HIV infection to the healthy equilibrium point in the face of model uncertainty and external disturbances when compared to one of the newest control techniques.
[1] R. V. Culshaw, S. Ruan, and R. J. Spiteri, "Optimal HIV treatment by maximising immune response," J. of Mathematical Biology, vol. 48, no. 5, pp. 545-562, 2004.
[2] D. Y. Lu, H. Y. Wu, N. S. Yarla, B. Xu, J. Ding, and T. R. Lu, "HAART in HIV/AIDS treatments: future trends," Infectious Disorders-Drug Targets, vol. 18, no. 1, pp. 15-22, 2018.
[3] A. Sharafian, A. Sharifi, and W. Zhang, "Fractional sliding mode based on RBF neural network observer: application to HIV infection mathematical model," Computers & Mathematics with Applications, vol. 79, no. 11, pp. 3179-3188, 1 Jun. 2020.
[4] Z. Zhang, J. Zhang, F. Cheng, and F. Liu, "A novel stability criteria of a class nonlinear fractional-order HIV-1 system with multiple delay," International J. of Control, Automation and Systems, vol. 17, no. 9, pp. 2274-2283, Sept. 2019.
[5] R. S. Butt, I. Ahmad, R. Iftikhar, and M. Arsalan, "Integral backstepping and synergetic control for tracking of infected cells during early antiretroviral therapy," IEEE Access, vol. 7, pp. 69447-69455, 2019.
[6] H. Jahanshahi, "Smooth control of HIV/AIDS infection using a robust adaptive scheme with decoupled sliding mode supervision," The European Physical J. Special Topics, vol. 227, no. 7, pp. 707-718, 2018.
[7] A. J. Anelone and S. K. Spurgeon, "Prediction of the containment of HIV infection by antiretroviral therapy-a variable structure control approach," IET Systems Biology, vol. 11, no. 1, pp. 44-53, Feb. 2017.
[8] P. S. Rivadeneira and C. H. Moog, "Impulsive control of single-input nonlinear systems with application to HIV dynamics," Applied Mathematics and Computation, vol. 218, no. 17, pp. 8462-8474, 1 May 2012.
[9] Y. Pei, N. Shen, J. Zhao, Y. Yu, and Y. Chen, "Analysis and simulation of a delayed HIV model with reaction-diffusion and sliding control," Mathematics and Computers in Simulation, vol. 212, pp. 382-405, Oct. 2023.
[10] D. Shi, S. Ma, and Q. Zhang, "Sliding mode dynamics and optimal control for HIV model," Mathematical Biosciences and Engineering, vol. 20, no. 4, pp. 7273-7297, 13 Feb. 2023.
[11] A. Izadbakhsh, A. A. Kalat, and S. Khorashadizadeh, "Observer-based adaptive control for HIV infection therapy using the Baskakov operator," Biomedical Signal Processing and Control, vol. 65, Article ID: 102343, Mar. 2021.
[12] N. H. Jo, "Robust drug treatment for HIV-1 infection model with completely unknown parameters," International J. of Control, Automation and Systems, vol. 17, no. 12, pp. 3113-3121, Dec. 2019.
[13] Y. Ding, Z. Wang, and H. Ye, "Optimal control of a fractional-order HIV-immune system with memory," IEEE Trans. on Control Systems Technology, vol. 20, no. 3, pp. 763-769, May 2011.
[14] H. D. Kwon, J. Lee, and S. D. Yang, "Optimal control of an age-structured model of HIV infection," Applied Mathematics and Computation, vol. 219, no. 5, pp. 2766-2779, Nov. 2012.
[15] H. Wang, et al., "A Caputo-Fabrizio fractional-order model of HIV/AIDS with a treatment compartment: sensitivity analysis and optimal control strategies," Entropy, vol. 23, no. 5, Article ID: e23050610, 2021.
[16] E. A. Hernandez-Vargas, P. Colaneri, and R. H. Middleton, "Optimal therapy scheduling for a simplified HIV infection model," Automatica, vol. 49, no. 9, pp. 2874-2880, Sept. 2013.
[17] A. E. Abharian, S. Z. Sarabi, and M. Yomi, "Optimal sigmoid nonlinear stochastic control of HIV-1 infection based on bacteria foraging optimization method," Biomedical Signal Processing and Control, vol. 10, pp. 184-191, Mar. 2014.
[18] P. Di Giamberardino and D. Iacoviello, "LQ control design for the containment of the HIV/AIDS diffusion," Control Engineering Practice, vol. 77, pp. 162-173, Aug. 2018.
[19] N. A. Reisi, S. H. Lakmesari, M. J. Mahmoodabadi, and S. Hadipour, "Optimum fuzzy control of human immunodeficiency virus type1 using an imperialist competitive algorithm," Informatics in Medicine Unlocked, vol. 16, Article ID: 100241, 2019.
[20] M. H. A. Biswas, M. M. Haque, and U. K. Mallick, "Optimal control strategy for the immunotherapeutic treatment of HIV infection with state constraint," Optimal Control Applications and Methods, vol. 40, no. 4, pp. 807-818, Jul./Aug. 2019.
[21] S. B. Chen, et al., "Antiretroviral therapy of HIV infection using a novel optimal type-2 fuzzy control strategy," Alexandria Engineering J., vol. 60, no. 1, pp. 1545-1555, Feb. 2021.
[22] E. Shamsara, Z. Afsharnezhad, and S. Effati, "Optimal drug control in a four‐dimensional HIV infection model," Optimal Control Applications and Methods, vol. 41, no. 2, pp. 469-486, Mar./ Apr. 2020.
[23] T. Jang, H. D. Kwon, and J. Lee, "Free terminal time optimal control problem of an HIV model based on a conjugate gradient method," Bulletin of Mathematical Biology, vol. 73, no. 10, pp. 2408-2429, Oct. 2011.
[24] P. Di Giamberardino and D. Iacoviello, "HIV infection control: a constructive algorithm for a state-based switching control," International J. of Control, Automation and Systems, vol. 16, no. 3, pp. 1469-1473, Jun. 2018.
[25] F. Sun and K. Turkoglu, "Estimation of CD4+T cell count parameters in HIV/AIDS patients based on real-time nonlinear receding horizon control," International J. of Control, Automation and Systems, vol. 16, no. 4, pp. 1805-1813, Aug. 2018.
[26] G. Pannocchia, M. Laurino, and A. Landi, "A model predictive control strategy toward optimal structured treatment interruptions in anti-HIV therapy," IEEE Trans. on Biomedical Engineering, vol. 57, no. 5, pp. 1040-1050, May 2010.
[27] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Society for Industrial and Applied Mathematics, 2000.
[28] Q. Liu and J. Wang, "A one-layer recurrent neural network with a discontinuous activation function for linear programming," Neural Computation, vol. 20, no. 5, pp. 1366-1383, May 2008.
[29] Y. Xia and J. Wang, "A bi-projection neural network for solving constrained quadratic optimization problems," IEEE Trans. on Neural Networks and Learning Systems, vol. 27, no. 2, pp. 214-224, Feb. 2015.
[30] A. Golbabai and S. Ezazipour, "A projection-based recurrent neural network and its application in solving convex quadratic bilevel optimization problems," Neural Computing and Applications, vol. 32, no. 8, pp. 3887-3900, Apr. 2020.
[31] Y. Xia, J. Wang, and W. Guo, "Two projection neural networks with reduced model complexity for nonlinear programming," IEEE Trans. on Neural Networks and Learning Systems, vol. 31, no. 6, pp. 2020-2029, Jun. 2019.
[32] Y. Yang and X. Xu, "The projection neural network for solving convex nonlinear programming," in Proc. Int. Conf. on Intelligent Computing, Springer, pp. 174-181, Qingdao, China, 21-24 Aug. 2007.
[33] Q. Liu and J. Wang, "A projection neural network for constrained quadratic minimax optimization," IEEE Trans. on Neural Networks and Learning Systems, vol. 26, no. 11, pp. 2891-2900, Nov. 2015.
[34] Y. Zhang, S. Chen, S. Li, and Z. Zhang, "Adaptive projection neural network for kinematic control of redundant manipulators with unknown physical parameters," IEEE Trans. on Industrial Electronics, vol. 65, no. 6, pp. 4909-4920, Jun. 2017.
[35] M. Yang, Y. Zhang, and H. Hu, "Posture coordination control of two-manipulator system using projection neural network," Neurocomputing, vol. 427, pp. 179-190, Feb. 2021.
[36] Z. Li, H. Xiao, C. Yang, and Y. Zhao, "Model predictive control of nonholonomic chained systems using general projection neural networks optimization," IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 45, no. 10, pp. 1313-1321, Oct. 2015.
[37] N. H. Jo and Y. Roh, "A two-loop robust controller for HIV infection models in the presence of parameter uncertainties," Biomedical Signal Processing and Control, vol. 18, pp. 245-253, Apr. 2015.
[38] H. Shim, N. H. Jo, H. Chang, and J. H. Seo, "A system theoretic study on a treatment of AIDS patient by achieving long-term non-progressor," Automatica, vol. 45, no. 3, pp. 611-622, Mar. 2009.
[39] Z. Hou and S. Xiong, "On model-free adaptive control and its stability analysis," IEEE Trans. on Automatic Control, vol. 64, no. 11, pp. 4555-4569, Nov. 2019.
[40] H. Du, X. Yu, M. Z. Chen, and S. Li, "Chattering-free discrete-time sliding mode control," Automatica, vol. 68, pp. 87-91, Jun. 2016.
[41] Y. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Trans. on Neural Networks, vol. 9, no. 6, pp. 1331-1343, Nov. 1998.
[42] S. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its KWTA application," IEEE Trans. on Neural Networks, vol. 17, no. 6, pp. 1500-1510, Nov. 2006.
[43] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, New York: Wiley, vol. 2, 2007.
[44] C. D. Meyer, Matrix Analysis and Applied Linear Algebra, vol. 71, SIAM, 2000.
[45] M. J. Mahmoodabadi and S. H. Lakmesari, "Adaptive sliding mode control of HIV-1 infection model," Informatics in Medicine Unlocked, vol. 25, Article ID: 100703, 2021.
