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## Design of Optimal Sliding Mode Control based on Linear Matrix Inequality for Fractional Time-Varying Delay Systems | ||

International Journal of Industrial Electronics Control and Optimization | ||

دوره 5، شماره 4، اسفند 2022، صفحه 317-325 اصل مقاله (816.77 K) | ||

نوع مقاله: Research Articles | ||

شناسه دیجیتال (DOI): 10.22111/ieco.2022.42132.1423 | ||

نویسندگان | ||

Mohammad Ghamgosar^{1}؛ Seyed Mehdi Mirhosseini-Alizamini^{*} ^{2}؛ Mahmood Dadkhah^{3}
| ||

^{1}Department of Matematics, Payame Noor University (PNU), Tehran, Iran | ||

^{2}Department of Mathematics, Payame Noor University (PNU), Tehran, Iran | ||

^{3}Department of Mathematics, Payame Noor University (PNU), Theran, Iran | ||

چکیده | ||

This paper considers an optimal sliding mode control based on the cost control guaranteed approach using the linear quadratic regulator method to stabilize delay fractional under involved disturbance. We propose an approach to an open research problem in the design of an LMI-based sliding mode controller in which there are some constraints such as optimizing system performance. The sliding mode technique is well-known as an effective tool for calculating the transient response of the system and achieving robust system performance. LQR classic techniques are less effective for studying an optimal fractional system in the presence of disturbance due to nonlinearity, so we use the optimal sliding mode approach control law designed for the nominal system and, then, combined it with a fractional sliding mode controller. By using the Razumikhin theorem for the stability of fractional order systems with delay and linear matrix inequality, conditions on asymptotically stabilization were obtained . The presented controller stabilizes the nominal system and guarantees an adequate level of system performance. The sliding mode controller presented in the article, in addition to eliminating the effect of disturbance in the system, is independent of the delay A numerical example was provided to illustrate the effectiveness of the main results. | ||

کلیدواژهها | ||

Delay Systems؛ Integral sliding mode؛ Linear quadratic regulator؛ Fractional order systems | ||

مراجع | ||

[1] M. Imani, U.M. Braga, and S. Xiao, " Finite-horizon LQR controller for partially observed Boolean dynamical systems," Automatica, Vol. 95, pp. 172–179, 2018.
[2] S. M. Mirhosseini-Alizamani, "Solving linear optimal control problems of the time-delayed systems by Adomian decomposition method," Iranian Journal of Numerical Analysis of Optimization, Vol.9, No. 2, , pp. 165-185,2019.
[3] S. M. Mirhosseini-Alizamani, S. Effati and A. Heydari, "An iterative method for suboptimal control of a class of nonlinear time-delayed systems," Systems and Control Letters, Vol. 82, pp. 40-50, 2015. [4] R. Sakthivel , B. Kaviarasan , P.Selvaraj and H.R. Karimi , "EID based sliding mode investment policy design for fuzzy stochastic jump financial systems," Nonlinear Analysis: Hybrid Systems, pp. 100–108, 2018. [5] M. Li, J. Wang, "Finite time stability of fractional delay differential equations," Applied Mathematics Letters, Vol. 64, pp. 170-176, 2017. [6] Y. Han , Y. Kao, C. Gao, J. Zhao and C.Wang , "H∞ sliding mode control of discrete switched systems with time-varying delays," ISA Trans, pp. 12–19, 2019. [7] S. Haghighatnia , H.T. Shandiz, and A. Alfi, " Conformable Fractional Order Sliding Mode Control for a Class of Fractional Order Chaotic Systems," International Journal of Industrial Electronics, Control and Optimization, Vol. 2, pp. 177-188, 2019. [8] Y.H Lan , L.L . Wang and C.X. Chen , "Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control," J Optim Theory Appl, Vol. 174, pp. 197–209, 2017. [9] R. Sedaghati , M.R. Shakarami,, " A New Sliding Mode- Based Power Sharing Control Method for Multiple Energy Sources in the Microgrid under Different Conditions," International Journal of Industrial Electronics, Control and Optimization, Vol. 2, pp. 25-38, 2019. [10] S.S. Shamsabad Farahani , S. Fakhimi Derakhshan,, " LMIbased Congestion Control Algorithms for a Delayed Network," International Journal of Industrial Electronics, Control and Optimization, Vol. 2, pp. 91-98, 2019. [11] Y. B. Shtessel, I. A. Shkolnikov and M. D. J. Brown, "An asymptotic second order smooth sliding mode control," Asian Journal of Control, Vol. 5, pp. 498–504, 2003. [12] M. Li, J. Wang, "Finite time stability of fractional delay differential equations," Applied Mathematics Letters, Vol. 64, pp. 170-176, 2017. [13] J. Li, X. Guo, C. Chen and Q. Su, "Robust fault diagnosis for switched systems based on sliding mode observer," Applied Mathematics and Computation, Vol. 341, pp. 193–203, 2019. [14] A. Si-Ammour, S. Djennoune, and M. Bettayeb, "A sliding mode control for linear fractional systems with input and state delays,” Commun Nonlinear Sci Numer Simulat, Vol.14, pp. 2310–2318, 2009. [15] H. Zhang, L. Cao and S. Tang, " Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR," International Journal of Advanced Robotic Systems, Vol. 14 , pp. 367-377, 2017.
[16] M. H. Heydari, M. Razzaghi, " Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems," International Journal of Systems Science , , Vol. 53, 2022. [17] M.H. Heydari, M.Razzaghi,, " A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative," Chaos, Solitons & Fractals, Vol. 152, 2021. [18] K. Mathiyalagan, G. Sangeetha, "Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control," control, Journal of the Franklin Institute, Vol. 356, No. 7, pp. 3948-3964, 2019. [19] S.D. Mulje, R.M. Nagarale, "LQR Technique based Second Order Sliding Mode Control for Linear Uncertain Systems," International Journal of Computer Applications , Vol. 137, pp. 8887–975, 2016. [20] D. T. Hong, N. H. Sau, "Output feedback finite-time dissipative control for uncertain nonlinear fractional-order systems," Asian Journal of Control, pp. 1–10, 2021. [21] M. V. Thuan, N. H. Sau, N. T. T. Huyen, "Finite-time H∞ control of uncertain fractional-order neural Networks," Computational and Applied Mathematics, Vol. 59, pp. 39-59, 2020. [22] B. B. He, H. C. Zhou, C. H. Kou and Y. Chen, "Stabilization of uncertain fractional order system with time varying delay using BMI approach," Asian Journal of Control, Vol. 53,2019. [23] K. Mathiyalagan, G. Sangeetha, "Second-order sliding mode control for nonlinear fractional-order systems," Applied Mathematics and Computation, Vol. 383, 2020. [24] V. Phat, P. Niamsup and M. V. Thuan, " New Criteria for Guaranteed Cost Control of Nonlinear Fractional-Order Delay Systems: a Razumikhin Approach, " Vietnam J.Mah, Vol. 47, pp. 403–415 ,2019. [25] A.A. Kilbas , H.M. Srivastava and Trujillo J.J., "Theory and Application of Fractional Differential Equations," Elsevier, New York, 2006. [26] M.A. Duarte-Mermoud , N. Aguila-Camacho , J.A. Gallegos and R. Castro-Linares, "Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems," Communications in Nonlinear Science and Numerical Simulation, pp. 650–659, 2015. [27] L. Chen, R. Wu, Y. Cheng and Y. Chen, "Delay dependent and order dependent stability and stabilization of fractional order linear systems with time varying delay," IEEE Transactions on Circuits and Systems II: Express Briefs, 2019. [28] S. Liu, W. Jiang and X. Zhou, " Lyapunov stability analysis of fractional nonlinear systems,” Applied Mathematics Letters, Vol. 51, pp. 13-19, 2015. [29] H. Shen , F. Li , J. Cao J., Z.G. Wu and G. Lu , "Fuzzymodel- based output feedback reliable control for networkbased semi-Markov jump nonlinear systems subject to redundant channels," IEEE Transactions on Cybernetics, 2019. [30] D. Sierociuk, B.M. Vinagre, "Infinite Horizon Statefeedback LQR Controller for Fractional Systems," 49th IEEE Conference on Decision and Controls, pp. 15-17,2010. [31] M. Thuan, D. C. Huong, "New Results on Stabilization of Fractional-Order Nonlinear Systems via an LMI Approach," Asian Journal of Control, Vol. 20, No. 4, pp.1541-1550, 2018. [32] C. Yin, Y. Chen and S. Zhong, "LMI based design of a sliding mode controller for a class of uncertain fractional order nonlinear systems," American Control Conference (ACC), pp. 6526-6531, 2013. | ||

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