دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,370
تعداد مقالات16,844
تعداد مشاهده مقاله54,232,672
تعداد دریافت فایل اصل مقاله16,943,927
Shokouhi, Tahereh, Allahdadi, Mahdi, Soradi zeid, Samaneh. (1403). Optimal control of fractional differential equations with interval uncertainty. سامانه مدیریت نشریات علمی, 13(2), 538-553. doi: 10.22034/cmde.2024.60642.2597
Tahereh Shokouhi; Mahdi Allahdadi; Samaneh Soradi zeid. "Optimal control of fractional differential equations with interval uncertainty". سامانه مدیریت نشریات علمی, 13, 2, 1403, 538-553. doi: 10.22034/cmde.2024.60642.2597
Shokouhi, Tahereh, Allahdadi, Mahdi, Soradi zeid, Samaneh. (1403). 'Optimal control of fractional differential equations with interval uncertainty', سامانه مدیریت نشریات علمی, 13(2), pp. 538-553. doi: 10.22034/cmde.2024.60642.2597
Shokouhi, Tahereh, Allahdadi, Mahdi, Soradi zeid, Samaneh. Optimal control of fractional differential equations with interval uncertainty. سامانه مدیریت نشریات علمی, 1403; 13(2): 538-553. doi: 10.22034/cmde.2024.60642.2597

Optimal control of fractional differential equations with interval uncertainty

Computational Methods for Differential Equations
مقاله 13، دوره 13، شماره 2، خرداد 2025، صفحه 538-553    اصل مقاله (864.14 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60642.2597
نویسندگان
Tahereh Shokouhi1؛ Mahdi Allahdadi* 1؛ Samaneh Soradi zeid2
1Mathematics Faculty‎, ‎University of Sistan and Baluchestan‎, ‎Zahedan‎, ‎Iran.
2Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran.
چکیده
The purpose of this paper is to obtain numerical solutions of fractional interval optimal control problems. To do so, first, we obtain a system of fractional interval differential equations through necessary conditions for the optimality of these problems, via the interval calculus of variations in the presence of interval constraint arithmetic. Relying on the trapezoidal rule, we obtain a numerical approximation for the interval Caputo fractional derivative. This approach causes the obtained conditions to be converted to a set of algebraic equations which can be solved using an iterative method such as the interval Gaussian elimination method and interval Newton method. Finally, we solve some examples of fractional interval optimal control problems in order to evaluate the performance of the suggested method and compare the past and present achievements in this manuscript.
کلیدواژه‌ها
Interval optimal control problems؛ Interval fractional calculus؛ Fractional interval differential equation؛ Interval iterative method؛ Interval arithmetic
مراجع
  • [1] R. P. Agarwal, S. Arshad, D. ORegan, and V. Lupulescu,´ A Schauder fixed point theorem in semilinear spaces and applications, Fixed point Theorey Appl., 2013 (2013), 1-13.
  • [2] R. P. Agarwal, S. Arshad, D. ORegan, and V. Lupulescu,´ Fuzzy fractional integral equations under compactness type condition, Fract. Calc. Appl. Anal., 15 (2012), 572-590.
  • [3] R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72(6) (2010), 2859-2862.
  • [4] Z. Alijani, D. Baleanu, B. Shiri, and G. C. Wu, Spline collocation methods for systems of fuzzy fractional differential equations, Chaos, Solitons Fractals, 131 (2020), 109510.
  • [5] M. Alipour and S. Soradi Zeid, Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method, Computational Methods for Differential Equations, 11 (2023), 52-64.
  • [6] M. Allahdadi, S. Soradi-Zeid, and T. Shokouhi, Accurate solutions of interval linear quadratic regulator optimal control problems with fractional-order derivative, Soft Comput., (2023), 1-18.
  • [7] T. Allahviranloo, S. Salahshour, and S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Comput., 16 (2012), 297-302.
  • [8] T. V. An, N. D. Phu, and N. Van Hoa, A survey on non-instantaneous impulsive fuzzy differential equations involving the generalized Caputo fractional derivative in the short memory case, Fuzzy Sets Syst., 443 (2022), 160-197.
  • [9] S. Arshad and V. Lupulescu, Fractional differential equation with the fuzzy initial condition, Electron. J. Differ. Equations, 2011 (2011), 1-8.
  • [10] S. Arshad and V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal., Theory Methods Appl., 74 (2011), 3685-3693.
  • [11] F. B. Bergamaschi and R. H. N. Santiago, A Study on Constrained Interval Arithmetic. In Explainable AI and Other Applications of Fuzzy Techniques: Proceedings of the 2021 Annual Conference of the North American Fuzzy Information Processing Society, NAFIPS 2021, Springer International Publishing, (2022), 26-36.
  • [12] Y. Chalco-Cano, W. A. Lodwick, and B. Bede, Single level constraint interval arithmetic, Fuzzy Sets Syst., 257 (2014), 146-168.
  • [13] R. Dehghan and M. Kianpour,, Using positive semi-definite optimization to solve the problem of optimal control of control systems of isothermal continuous stirred tank reactors, J. Oper. Res. Appl., 52 (2017), 1-13.
  • [14] K. Diethelm, N. J. Ford, A. D. Freed, and Y. Luchko, Algorithms for the fractional calculus: a selection of numerical methods, Comput. Methods Appl. Mech. Eng., 194 (2005), 743-773.
  • [15] N. Eqra, R. Vatankhah, and M. Eghtesad, A novel adaptive multi-critic based separated-states neuro-fuzzy controller: Architecture and application to chaos control, ISA. transactions, 111 (2021), 57-70.
  • [16] B. Farhadinia, Pontryagin’s minimum principle for fuzzy optimal control problems, Iran. J. Fuzzy Syst., 11 (2014), 27-43.
  • [17] J. Garloff, Interval Gaussian elimination with pivot tightening, SIAM J. Matrix Anal. Appl., 30(4) (2009), 17611772.
  • [18] E. R. Hansen and R. I. Greenberg, An interval Newton method, SIAM J. Matrix Anal. Appl., 12(2-3) (1983), 89-98.
  • [19] M. K. Kar, A. K. Singh, S. Kumar, and B. Rout, Application of Fractional-Order PID Controller to Improve Stability of a Single-Machine Infinite-Bus System, J. Instit. Engin., (India): Series B, 105(1) (2024), 77-92.
  • [20] S. Kuntanapreeda and P. M. Marusak, Nonlinear extended output feedback control for CSTRs with van de Vusse reaction, Computers & Chemical Engineering, 41 (2012), 10-23.
  • [21] W. A. Lodwick, Constrained interval arithmetic. Denver: University of Colorado at Denver, Center for Comput. Math., 1999.
  • [22] W. A. Lodwick, Interval and fuzzy analysis: A unified approach, Adv. Imaging Electron. Phys., 148 (2007), 76192.
  • [23] V. Lupulescu, Fractional calculus for interval-valued functions, Fuzzy Sets Syst., 265 (2014), 63-85.
  • [24] V. Lupulescu and N. Van Hoa, Interval Abel integral equation, Soft Comput., 21(10) (2017), 2777-2784.
  • [25] S. Maitama and W. Zhao, Homotopy analysis Shehu transform method for solving fuzzy differential equations of fractional and integer order derivatives, Comput. Appl. Math., 40 (2021), 1-30.
  • [26] S. Markov, Calculus for interval functions of a real variable, Comput., 22(4) (1979), 325-337.
  • [27] M. Mazandarani and A. V. Kamyad, Modified fractional Euler method for solving fuzzy fractional initial value problem, Commun. Nonlinear Sci. Numer. Simul., 18(1) (2013), 12-21.
  • [28] S. Mohammadi and S. R. Hejazi, Presentation of the model and optimal control of non-linear fractional-order chaotic system of glucose-insulin, Comput. Methods Biomech. Biomed. Eng., 27 (7) (2024), 836-848.
  • [29] A. Mohammed, Z. T. Gong, and M. Osman, A Numerical Technique for Solving Fuzzy Fractional Optimal Control Problems, J. Comput. Anal. Appl., 3 (2021), 413-430.
  • [30] A. M. Mustafa, Z. T. Gong, and M. Osman, The solution of fuzzy variational problem and fuzzy optimal control problem under granular differentiability concept, Int. J. Comput. Math., 98(8) (2021), 1495-520.
  • [31] M. D. Patil, K. Vadirajacharya, and S. W. Khubalkar, Design and tuning of digital fractional-order PID controller for permanent magnet DC motor, IETE. J. Research, 69(7) (2023), 4349-4359.
  • [32] S. Pooseh, R. Almeida, and D. F. Torres, Fractional order optimal control problems with free terminal time, J. Ind. Manage. Optim., 10(2)(2014), 363-381.
  • [33] S. Sabermahani and Y. Ordokhani, Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method, J. Vib. Control, 30(1-2) (2024), 418-432.
  • [34] S. Salahshour, T. Allahviranloo, and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17(3) (2012), 1372-1381.
  • [35] S. Salahshour, T. Allahviranloo, S. Abbasbandy, and D. Baleanu, Existence and uniqueness results for fractional differential equations with uncertainty, Adv. Differ. Equations, 2012 (2012), 1-12.
  • [36] N. Van Hoa, Existence results for extremal solutions of interval fractional functional integro-differential equations, Fuzzy Sets Syst., 347 (2018), 29-53.
  • [37] H. Vu, V. Lupulescu, and N. Van Hoa, Existence of extremal solutions to interval-valued delay fractional differential equations via monotone iterative technique, J. Intell. Fuzzy Syst., 34(4) (2018), 2177-2195.
  • [38] H. Wang, R. Rodrguez-Lpez, and A. Khastan, On the stopping time problem of interval-valued differential equations under generalized Hukuhara differentiability, Inf. Sci., 579 (2021), 776-795.
  • [39] T. Wang, A. San-Millan, and S. S. Aphale, Quantifying the performance enhancement facilitated by fractionalorder implementation of classical control strategies for nanopositioning, ISA. transactions, 2024.
  • [40] X. Xia and T. Li, A fuzzy control model based on BP neural network arithmetic for optimal control of smart city facilities, Pers. Ubiquitous Comput., 23 (2019), 453-463.
  • [41] C. Yang, W. Lu, and Y. Xia, Positioning accuracy analysis of industrial robots based on non-probabilistic timedependent reliability, IEEE. Trans. Reliab., 2023.
  • [42] C. Yang, W. Lu, and Y. Xia, Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis, Reliab. Eng. Syst. Saf., 237 (2023), 109382.
  • [43] C. Yang and Y. Xia, Interval Pareto front-based multi-objective robust optimization for sensor placement in structural modal identification, Reliab. Eng. Syst. Saf., 242 (2024), 109703.
  • [44] C. Yang and Y. Xia, Interval uncertainty-oriented optimal control method for spacecraft attitude control, IEEE. Trancs. Aerosp. Electron. Syst., 2023.
  • [45] T. Zhou, Z. Yuan, and T. Du, On the fractional integral inclusions having exponential kernels for interval-valued convex functions, Math. Sci., 17(2) (2023), 107-120.
آمار
تعداد مشاهده مقاله: 174
تعداد دریافت فایل اصل مقاله: 346


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب