
تعداد نشریات | 33 |
تعداد شمارهها | 770 |
تعداد مقالات | 7,474 |
تعداد مشاهده مقاله | 12,463,586 |
تعداد دریافت فایل اصل مقاله | 8,475,980 |
Controllability Criteria for Type-2 Fuzzy Fractional-order Dynamical System via Mittag-Leffler Matrix Function using granular derivative. | ||
Iranian Journal of Fuzzy Systems | ||
دوره 21، شماره 5، آذر و دی 2024، صفحه 133-150 اصل مقاله (702.53 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2024.47862.8422 | ||
نویسندگان | ||
Srilekha R؛ Parthiban V* ؛ Dhanasekar sundaram | ||
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India. | ||
چکیده | ||
This study is concerned with finding the controllability of granular type-2 fuzzy fractional-order dynamical control systems (GrT2FuFDCS) using Mittag-Leffler matrix function. Some new concepts concerning to granular interval valued type-2 fuzzy fractional derivative is introduced in this paper. To arrive at finding the controllability of the type-2 fuzzy dynamical system, type-2 triangular fuzzy function and type-2 triangular fuzzy numbers are used to model fractional dynamical control system. Besides, the controllability Grammian matrix is defined based on Mittag-Leffler matrix function. Granular fuzzy Laplace transform and inverse Laplace transform are utilized to derive the solution of the type- 2 triangular fuzzy fractional-order control systems. The derived results ensure that the controllability of the proposed GrT2FuFDCS for both linear and non-linear case exists. Finally, numerical examples and their simulation results are given to illustrate the merit of the obtained results. | ||
کلیدواژهها | ||
Horizontal membership function؛ Type-2 triangular fuzzy number؛ Type-2 fuzzy granular Laplace transform؛ Type-2 fuzzy fractional differential equations, Granular differentiability؛ Granular fuzzy fractional derivative؛ Type-2 fuzzy fractional granular controllability | ||
مراجع | ||
``[1] R. Abdollahipour, K. Khandani, A. A. Jalali, Consensus of uncertain linear multi-agent systems with granular fuzzy dynamics, International Journal of Fuzzy Systems, 24(4) (2022), 1780-1792. https://doi.org/10.1007/ s40815-021-01237-0 [2] V. Angulo-Castillo, Y. Chalco-Cano, A. Khastan, E. J. Villamizar-Roa, Applications of generalized fixed points theorems to the existence of uncertain differential equations with finite delay, Iranian Journal of Fuzzy Systems, 17(6) (2020), 1-15.https://doi.org/10.22111/IJFS.2020.5597 [3] S. Arshad, On existence and uniqueness of solution of fuzzy fractional differential equations, Iranian Journal of Fuzzy Systems, 10(6) (2013), 137-151. https://doi.org/10.22111/ijfs.2013.1336 [4] K. Balachandran, V. Govindaraj, M. Rivero, J. J. Trujillo, Controllability of fractional damped dynamical systems, Applied Mathematics and Computation, 257 (2015), 66-73. https://doi.org/10.1016/j.amc.2014.12.059 [5] P. Balasubramaniam, J. P. Dauer, Controllability of semilinear stochastic evolution equations in Hilbert space, International Journal of Stochastic Analysis, 14(4) (2001), 329-339. https://doi.org/10.1155/S1048953301000296
[6] N. P. Dong, H. V. Long, A. Khastan, Optimal control of a fractional order model for granular SEIR epidemic with uncertainty, Communications in Nonlinear Science and Numerical Simulation, 88 (2020), 105312. https: //doi.org/10.1016/j.cnsns.2020.105312 [7] B. Dubey, R. K. George, Controllability of linear time-invariant dynamical systems with fuzzy initial condition, In Proceedings of the World Congress on Engineering and Computer Science, 2 (2013). https://www.iaeng.org/ publication/WCECS2013/WCECS2013_pp879-884.pdf [8] Y. C. Kwun, Y. B. Kim, J. S. Park, Controllability for the impulsive semilinear fuzzy intergrodifferential equation in n-dimension fuzzy vector space, In 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery, 6 (2009), 162-166. https://doi.org/10.1109/FSKD.2009.645 9] L. H. Lan, Stability analysis for a class of Takagi-Sugeno fuzzy control systems with PID controllers, International Journal of Approximate Reasoning, 461 (2007), 109-119. https://doi.org/10.1016/j.ijar.2006.09.003 [10] R. Mastiani, S. Effati, On controllability and observability of fuzzy control systems, Iranian Journal of Fuzzy Systems, 15(6) (2018), 41-64. https://doi.org/10.22111/IJFS.2018.4364 [11] M. Mazandarani, M. Najariyan, Type-2 fuzzy fractional derivatives, Communications in Nonlinear Science and Numerical Simulation, 19(7) (2014), 2354-2372. https://doi.org/10.1016/j.cnsns.2013.11.003 [12] M. Mazandarani, M. Najariyan, Differentiability of type-2 fuzzy number-valued functions, Communications in Nonlinear Science and Numerical Simulation, 19(3) (2014), 710-725. https://doi.org/10.1016/j.cnsns.2013. 07.002 [13] M. Mazandarani, M. Najariyan, A note on “A class of linear differential dynamical systems with fuzzy initial condition”, Fuzzy Sets and Systems, 265 (2015), 121-126. https://doi.org/10.1016/j.fss.2014.05.018 [14] M. Mazandarani, J. Pan, The challenges of modeling using fuzzy standard interval arithmetic: A case study in electrical engineering, Information Sciences, 653 (2024), 119774. https://doi.org/10.1016/j.ins.2023.119774 [15] M. Mazandarani, N. Pariz, A. V. Kamyad, Granular differentiability of fuzzy-number-valued functions, IEEE Transactions on Fuzzy Systems, 26(1) (2017), 310-323. https://doi.org/10.1109/TFUZZ.2017.2659731 [16] M. Mazandarani, L. Xiu, A review on fuzzy differential equations, IEEE Access, 9 (2021), 62195-62211. https: //doi.org/10.1109/ACCESS.2021.3074245 [17] M. Mazandarani, L. Xiu, Interval type-2 fractional fuzzy inference systems: Towards an evolution in fuzzy inference systems, Expert Systems with Applications, 189 (2022), 115947. https://doi.org/10.1016/j.eswa.2021.115947 [18] J. M. Mendel, F. Liu, On new quasi-type-2 fuzzy logic systems, In 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008, 354-360. https://doi.org/10.1109/FUZZY. 2008.4630390 [19] H. Mo, F. Y. Wang, M. Zhou, R. Li, Z. Xiao, Footprint of uncertainty for type-2 fuzzy sets, Information Sciences, 272 (2014), 96-110. https://doi.org/10.1016/j.ins.2014.02.092 [20] H. Mo, X. Zhao, F. Y. Wang, Application of interval type-2 fuzzy sets in unmanned vehicle visual guidance, International Journal of Fuzzy Systems, 21 (2019), 1661-1668. https://doi.org/10.1007/s40815-019-00680-4 [21] M. Muslim, A. Kumar, Controllability of fractional differential equation of order α ∈ (1, 2] with non-instantaneous impulses, Asian Journal of Control, 20(2) (2018), 935-942. https://doi.org/10.1002/asjc.1604 [22] A. M. Mustafa, Z. Gong, M. Osman, The solution of fuzzy variational problem and fuzzy optimal control problem under granular differentiability concept, International Journal of Computer Mathematics, 98(8) (2021), 1495-1520. https://doi.org/10.1080/00207160.2020.1823974 [23] M. Najariyan, M. Mazandarani, R. John, Type-2 fuzzy linear systems, Granular Computing, 2 (2017), 175-186. https://doi.org/10.1007/s41066-016-0037-y [24] M. Najariyan, L. Qiu, Interval type-2 fuzzy differential equations and stability, IEEE Transactions on Fuzzy Systems, 30(8) (2021), 2915-2929. https://doi.org/10.1109/TFUZZ.2021.3097810 [25] M. Najariyan, Y. Zhao, Fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives, IEEE Transactions on Fuzzy Systems, 26(4) (2017), 2273-2288. https://doi.org/10.1109/TFUZZ.2017.2783895 [26] M. Najariyan, Y. Zhao, On the stability of fuzzy linear dynamical systems, Journal of the Franklin Institute, 357(9) (2020), 5502-5522. https://doi.org/10.1016/j.jfranklin.2020.02.023 [27] M. Najariyan, Y. Zhao, Granular fuzzy fractional descriptor linear systems under granular caputo fuzzy fractional derivative, Soft Computing, 27(15) (2023), 10457-10467. https://doi.org/10.1007/s00500-023-08549-3 [28] N. D. Phu, L. Q. Dung, On the stability and controllability of fuzzy control set differential equations, International Journal of Reliability and Safety, 5(3-4) (2011), 320-335. https://doi.org/10.1504/IJRS.2011.041183 [29] A. Piegat, M. Landowski, Horizontal membership function and examples of its applications, International Journal of Fuzzy Systems, 17 (2015), 22-30. https://doi.org/10.1007/s40815-015-0013-8 [30] A. Piegat, M. Landowski, On fuzzy RDM-arithmetic, In Hard and Soft Computing for Artificial Intelligence, Multimedia and Security, 3-16 (2017). https://doi.org/10.1007/978-3-319-48429-7 [31] A. Piegat, M. Pluci´nski, Fuzzy number addition with the application of horizontal membership functions, The Scientific World Journal 2015, 1 (2015), 367214. https://doi.org/10.1155/2015/367214 [32] J. Priyadharsini, P. Balasubramaniam, Solvability of fuzzy fractional stochastic Pantograph differential system, Iranian Journal of Fuzzy Systems, 19(1) (2022), 47-60. https://doi.org/10.22111/IJFS.2022.6550 [33] N. T. K. Son, H. V. Long, N. P. Dong, Fuzzy delay differential equations under granular differentiability with applications, Computational and Applied Mathematics, 38(3) (2019), 107. https://doi.org/10.1007/ s40314-019-0881-x [34] K. Tomaszewska, A. Piegat, Application of the horizontal membership function to the uncertain displacement calculation of a composite massless rod under a tensile load, Soft Computing in Computer and Information Science, (2015), 63-72. https://doi.org/10.1007/978-3-319-15147-2_6 [35] I. Ucal Sari, C. Kahraman, Interval type-2 fuzzy capital budgeting, International Journal of Fuzzy Systems, 17(4) (2015), 635-646. https://doi.org/10.1007/s40815-015-0040-5 [36] H. Yang, Y. Chen, Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability, Communications in Nonlinear Science and Numerical Simulation, 133 (2024), 107984. https: //doi.org/10.1016/j.cnsns.2024.107984 [37] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65) 90241-X | ||
آمار تعداد مشاهده مقاله: 115 تعداد دریافت فایل اصل مقاله: 161 |