اخبار و اعلانات

 آمار

تعداد نشریات47
تعداد شماره‌ها1,232
تعداد مقالات10,580
تعداد مشاهده مقاله21,182,358
تعداد دریافت فایل اصل مقاله14,276,864
Rashki-Ghalehno, Mohammad, Mirhosseini-Alizamini, Seyed Mehdi, Naderi, Bashir. (1404). Robust Hybrid Adaptive Control via Enhanced Lyapunov Function for Chaotic Systems with Large Time Delays. فصلنامه علمی زیست فناوری گیاهان زراعی, (), -. doi: 10.30473/coam.2025.74158.1299
Mohammad Rashki-Ghalehno; Seyed Mehdi Mirhosseini-Alizamini; Bashir Naderi. "Robust Hybrid Adaptive Control via Enhanced Lyapunov Function for Chaotic Systems with Large Time Delays". فصلنامه علمی زیست فناوری گیاهان زراعی, , , 1404, -. doi: 10.30473/coam.2025.74158.1299
Rashki-Ghalehno, Mohammad, Mirhosseini-Alizamini, Seyed Mehdi, Naderi, Bashir. (1404). 'Robust Hybrid Adaptive Control via Enhanced Lyapunov Function for Chaotic Systems with Large Time Delays', فصلنامه علمی زیست فناوری گیاهان زراعی, (), pp. -. doi: 10.30473/coam.2025.74158.1299
Rashki-Ghalehno, Mohammad, Mirhosseini-Alizamini, Seyed Mehdi, Naderi, Bashir. Robust Hybrid Adaptive Control via Enhanced Lyapunov Function for Chaotic Systems with Large Time Delays. فصلنامه علمی زیست فناوری گیاهان زراعی, 1404; (): -. doi: 10.30473/coam.2025.74158.1299

Robust Hybrid Adaptive Control via Enhanced Lyapunov Function for Chaotic Systems with Large Time Delays

Control and Optimization in Applied Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 آبان 1404    اصل مقاله (2.05 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2025.74158.1299
نویسندگان
Mohammad Rashki-Ghalehno؛ Seyed Mehdi Mirhosseini-Alizamini؛ Bashir Naderi*
Department of Mathematics‎, ‎Payame Noor University (PNU)‎, ‎Iran
چکیده
This paper introduces a robust hybrid adaptive control framework for stabilizing chaotic systems under persistent, potentially large time delays. The controller is based on an enhanced Lyapunov–Krasovskii functional that integrates an energy-capturing integral term with a bounded trigonometric term. The integral term accounts for historical effects by quantifying cumulative energy over the delay period, while the trigonometric term attenuates nonlinear oscillations. Embedding these components in a single control law yields stabilization of all state variables to the equilibrium despite substantial delays. We establish Uniform Ultimate Boundedness, showing that trajectories enter a compact neighborhood of the equilibrium after a finite transient and subsequently converge. Adjustable gains enable practitioners to determine the convergence radius and the size of the attraction region according to practical requirements. The method is validated on the delayed Lorenz system; simulations with a 20-second delay demonstrate rapid convergence to a small neighborhood of the equilibrium, with the Lyapunov functional derivative remaining non-positive. A comparative study with established controllers underscores the proposed approach’s favorable trade-offs among computational cost, oscillation suppression, and explicit stability guarantees. Overall, the proposed framework delivers a practical, robust, and high-performance solution for controlling chaotic systems in the presence of large time delays.

تازه های تحقیق
  • Introduces an enhanced Lyapunov function and a novel hybrid adaptive controller within the Lyapunov–Krasovskii framework, combining: (i) an integral term to mitigate delay effects and (ii) a bounded trigonometric term to limit nonlinear oscillations and boost stability.
  • Provides a rigorous mathematical analysis establishing positive definiteness of the Lyapunov function and negative definiteness of its derivative, guaranteeing global convergence of state variables to the equilibrium under constant delays.
  • Demonstrates controller performance via simulations of the chaotic Lorenz system under both small and large delays (up to 20 seconds), showing a uniform reduction in system energy through outputs such as phase portraits and Lyapunov derivative plots.
  • Addresses delay- and nonlinearity-induced challenges by proposing mechanisms to suppress adverse effects and prevent oscillation amplification.
  • Illustrates practical applicability in real-world systems with processing or communication delays across sectors like power networks, chemical reactors, and IoT.
  • Acknowledges limitations and offers directions for future work to further improve efficiency and scalability.
کلیدواژه‌ها
Constant time delay‎؛ ‎Hybrid adaptive control‎؛ ‎Lyapunov function‎؛ ‎Asymptotic stability‎؛ ‎Practical stability
مراجع

[1] Allgöwer, F., Zheng, A. (Eds.). (2012). “Nonlinear model predictive control”, (Vol. 26). Birkhäuser.

[2] Alruwaily, Y., Kharrat, M. (2025). “Adaptive neural control approach for switched nonlinear discrete-time systems with actuator faults and input dead zone”. Discrete Dynamics in Nature and Society, 2025(1), 2364395, doi:https://doi.org/10.1155/ddns/2364395.

[3] Ang, J.S.R., Sun, C.T., Mizutani, E. (1997). “Neuro-fuzzy and soft computing–A computational approach to learning and machine intelligence [Book review]”. IEEE Transactions on Automatic Control, 42(10), 1482-1484, doi:https://doi.org/10.1109/TAC.1997.633847.

[4] Astolfi, D., Praly, L., Marconi, L. (2022). “Harmonic internal models for structurally robust periodic output regulation”. Systems & Control Letters, 161, 105154, doi:https://doi.org/10.1016/j.sysconle.2022.105154.

[5] Åström, K.J., Hägglund, T. (2006). “Advanced PID Control”. Research Triangle Park, NC: ISA.

[6] Bechlioulis, C.P., Rovithakis, G.A. (2008). “Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance”. IEEE Transactions on Automatic Control, 53(9), 2090-2099, doi:https://doi.org/10.1109/TAC.2008.929402.

[7] Boiko, I.M. (2011). “Analysis of chattering in sliding mode control systems with continuous boundary layer approximation of discontinuous control”. In: Proceedings of the 2011 American Control Conference, 757-762, IEEE, doi:https://doi.org/10.1109/ACC.2011.5990793.

[8] Bucci, M.A., Semeraro, O., Allauzen, A., Wisniewski, G., Cordier, L., Mathelin, L. (2019). “Control of chaotic systems by deep reinforcement learning”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2231), 20190351, doi:https://doi.org/10.1098/rspa.2019.0351.

[9] Devaney, R.L. (1989). “An Introduction to Chaotic Dynamical Systems”. 2nd ed., Redwood City, CA: Addison-Wesley.

[10] Ding, H., Qian, J., Tian, D., Zeng, Y. (2025). “Norm-based adaptive control with a novel practical predefined-time sliding mode for chaotic system synchronization”. Mathematics, 13(5), 748, doi: https://doi.org/10.3390/math13050748.

[11] Ebrahimipour, M., Nezhadhosein, S., Mirhosseini-Alizamini, S.M. (2024). “Optimal adaptive sliding mode control for a class of nonlinear affine systems”. Control and Optimization in Applied Mathematics, 9(2), 123-138, doi:https://doi.org/10.30473/coam.2023.67868.1236.

12] Edwards, C., Spurgeon, S.K. (1998). “Sliding mode control: Theory and applications”. Taylor & Francis, doi:https://doi.org/10.1201/9781498701822.

[13] Erbatur, K., Kaynak, O., Sabanovic, A., Rudas, I. (1996). “Fuzzy adaptive sliding mode control of a direct drive robot”. Robotics and Autonomous Systems, 19(2), 215-227, doi:https://doi.org/10.1016/S0921-8890(96)00049-8.

[14] Fan, H.-Y., Lampinen, J. (2003). “A trigonometric mutation operation to differential evolution”. Journal of  Global Optimization, 27(1), 105-129, doi:https://doi.org/10.1023/A:1024653025686.

[15] Feng, Y., Yu, X. (2009). “Sliding mode control of chaotic systems”. In: Control of Chaos in Nonlinear Circuits and Systems, 55-77.

[16] Flores-Padilla, M., Treesatayapun, C. (2024). “Data-driven adaptive controller based on hyperbolic cost function for non-affine discrete-time systems with variant control direction”. Applied System Innovation, 7(3), 38, doi:https://doi.org/10.3390/asi7030038.

[17] Fridman, E. (2014). “Introduction to time-delay systems: Analysis and control”. Birkhäuser Cham, doi:https://doi.org/10.1007/978-3-319-09393-2.

[18] Fridman, E., Shaked, U. (2002). “A descriptor system approach to H/sub /spl infin// control of linear time-delay systems”. IEEE Transactions on Automatic Control, 47(2), 253-270, doi:https://doi.org/10.1109/9.983353.

[19] Ge, S.S., Hong, F., Lee, T.H. (2004). “Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients”. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(1), 499-516, doi:https://doi.org/10.1109/TSMCB.2003.817055.

[20] Gee, S.S., Lee, T.H., Harris, C.J. (1998). “Adaptive neural network control of robotic manipulators”. World Scientific Series in Robotics and Intelligent Systems: Volume 19, doi:https://doi.org/10.1142/3774.

[21] Gholami, M., Mirhosseini-Alizamini, S., Heydari, A. (2025). “Designing a sliding mode controller for a class of multi-controller COVID-19 disease model”. Iranian Journal of Numerical Analysis and Optimization, 15(1), 27-53, doi:https://doi.org/10.22067/ijnao.2024.85859.1355.

[22] Grüne, L., Pannek, J. (2016). “Nonlinear model predictive control”. In: Nonlinear Model Predictive Control. Communications and Control Engineering. Springer, Cham, doi:https://doi.org/10.1007/978-3-319-46024-6_3.

[23] Gu, K., Kharitonov, V.L., Chen, J. (2003). “Stability of time-delay systems”. Birkhäuser Boston, MA, doi:https://doi.org/10.1007/978-1-4612-0039-0.

[24] Hornik, K., Stinchcombe, M., White, H. (1989). “Multilayer feedforward networks are universal approximators”. Neural Networks, 2(5), 359-366, doi:https://doi.org/10.1016/0893-6080(89)90020-8.

[25] Jiang, B., Li, J., Yang, S. (2022). “An improved sliding mode approach for trajectory following control of nonholonomic mobile AGV”. Scientific Reports, 12(1), 17763, doi:https://doi.org/10.1038/s41598-022-22697-w.

[26] Khaledi, G., Mirhosseini-Alizamini, S.M., Ghamgosar, M. (2025). “LQR technique-based SMC design for a class of uncertain time-delay Conic nonlinear systems”. Computational Methods for Differential Equations, 13(2), 505-523, doi:https://doi.org/10.22034/cmde.2024.57243.2394.

[27] Khalil, H.K. (2002). “Nonlinear Systems”. 3rd Edition, Prentice-Hall, Inc., Upper Saddle River.

[28] Khalili Amirabadi, R., Fard, O.S., Mansoori, A. (2021). “A novel fuzzy sliding mode control approach for chaotic systems”. Iranian Journal of Fuzzy Systems, 18(6), 133-150, doi:https//doi.org/10.22111/ijfs.2021.6338.

[29] Kharitonov, V.L. (2013). “Time-delay systems: Lyapunov functionals and matrices”. Birkhäuser Boston, MA, doi:https://doi.org/10.1007/978-0-8176-8367-2.

[30] Krasovskii, N.N. (1963). “Stability of Motion. Applications of Lyapunov’s second method to differential systems and equations with delay”. Stanford, CA: Stanford University Press.

[31] Lafay, J.F. (2013). “Delay systems: From theory to numerics and applications”. Tomas Vyhlidal, J.F. Lafay, R. Sipahi. Springer, pp.404, 2014, Advances in Delay and Dynamics, S.-I. Niculescu,978-3-319-01694-8, doi:https://dx.doi.org/10.1007/978-3-319-01695-5.

[32] Lakshmanan, M., Senthilkumar, D.V. (2011). “Dynamics of nonlinear time-delay systems”. Springer Berlin, Heidelberg, doi:https://doi.org/10.1007/978-3-642-14938-2.

[33] Lasri, R., Rojas, I., Pomares, H., Rojas, F. (2011). “A new methodology for adaptive fuzzy controller: Comparison performance against several control algorithms in a real-time control process”. In: Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011), 470-474, doi:https://doi.org/10.5220/0003647204700474.

[34] Lee, H., Utkin, V.I. (2007). “Chattering suppression methods in sliding mode control systems”. Annual Reviews in Control, 31(2), 179-188, doi:https://doi.org/10.1016/j.arcontrol.2007.08.001.

[35] Leister, D.D., Koeln, J.P. (2024). “Robust model predictive control for nonlinear discrete-time systems using iterative time-varying constraint tightening”. 2025 American Control Conference (ACC), Denver, CO, USA, 2025, pp. 71-78, doi:https://doi.org/10.23919/ACC63710.2025.11108089.

[36] Levant, A. (2010). “Chattering analysis”. IEEE Transactions on Automatic Control, 55(6), 1380-1389, doi:https://doi.org/10.1109/TAC.2010.2041973.

[37] Liang, Y., Zhang, D., Li, G., Wu, T. (2022). “Adaptive chattering-free PID sliding mode control for tracking problem of uncertain dynamical systems”. Electronics, 11(21), 3499, doi:https://doi.org/10.3390/electronics11213499.

[38] Lin, W., Lin, Y. (2024). “A Lyapunov-Krasovskii method for semiglobal stabilization of a class of time-delay nonlinear systems with uncontrollable linearization by linear feedback”. IEEE Transactions on Automatic Control, 69(6), 4110-4117, doi:https://doi.org/10.1109/TAC.2023.3347340.

[39] Liu, Y.J., Xu, F., Tang, L. (2023). “Tangent barrier Lyapunov function-based adaptive event-triggered control for uncertain flexible beam systems”. Automatica, 152, doi:https://doi.org/10.1016/j.automatica.2023.110976.

[40] Long, F., Jiang, L., He, Y., Wu, M. (2019). ”Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality“. Applied Mathematics and Computation, 357, 325-337, doi:https://doi.org/10.1016/j.amc.2019.04.004.

[41] Lorenz, E.N. (1963). “Deterministic nonperiodic flow”. Journal of the Atmospheric Sciences, 20(2), 130-141, doi:https://doi.org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2.

[42] Maciejowski, J.M., Huzmezan, M. (1997). “Predictive control”. In: Magni, JF., Bennani, S., Terlouw, J. (eds) Robust Flight Control. Lecture Notes in Control and Information Sciences, vol 224. Springer, Berlin, Heidelberg, doi:https://doi.org/10.1007/BFb0113856.

[43] Mayne, D.Q. et al. (2000). “Constrained model predictive control: Stability and optimality”. Automatica, 36(6), 789-814, doi:https://doi.org/10.1016/S0005-1098(99)00214-9.

[44] Medina, L., Guerra, G., Herrera, M., Guevara, L., Camacho, O. (2024). “Trajectory tracking for non-holonomic mobile robots: A comparison of sliding mode control approaches”. Results in Engineering, 22, doi:https://doi.org/10.1016/j.rineng.2024.102105.

[45] Michalewicz, Z. (1996). “Genetic Algorithms + Data Structures = Evolution Programs”. Springer Berlin, Heidelberg, doi:https://doi.org/10.1007/978-3-662-03315-9.

[46] Michiels, W., Niculescu, S.-I. (2014). “Stability, control, and computation for time-delay systems: An eigenvalue-based approach”. Second Edition, SIAM, doi:https://doi.org/10.1137/1.9781611973631.

[47] Nicaise, S., Pignotti, C., Valein, J. (2011). “Exponential stability of the wave equation with boundary time-varying delay”. Discrete and Continuous Dynamical Systems-Series S, 4(3), 693-722, doi:https://doi.org/10.3934/dcdss.2011.4.693.

[48] Ott, E. (2002). “Chaos in Dynamical Systems”. 2nd Edition, Cambridge University Press, doi: https://doi.org/10.1017/CBO9780511803260.

[49] Otto, A., Just, W., Radons, G. (2019). “Nonlinear dynamics of delay systems: An overview”. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2153), 20180389, doi:https://doi.org/10.1098/rsta.2018.0389.

[50] Rawlings, J.B., Mayne, D.Q., Diehl, M. (2017). “Model predictive control: Theory, computation, and design”. vol. 2. Madison, WI: Nob Hill Publishing. [51] Richard, J.-P. (2003). “Time-delay systems: An overview of some recent advances and open problems”. Automatica, 39(10), 1667-1694, doi:https://doi.org/10.1016/S0005-1098(03)00167-5.

[52] Roldán-Caballero, A., Pérez-Cruz, J.H., Hernández-Márquez, E., García-Sánchez, J.R., Ponce-Silva, M., Rubio, J.D.J., Mendoza-Chegue, A. (2023). “Synchronization of a new chaotic system using adaptive control: Design and experimental implementation”. Complexity, 2023(1), doi:https://doi.org/10.1155/2023/2881192.

[53] Saeed, N.A., Saleh, H.A., El-Ganaini, W.A., Kamel, M., Mohamed, M.S. (2023). “On a new three-dimensional chaotic system with adaptive control and chaos synchronization”. Shock and Vibration, 2023(1), doi:https://doi.org/10.1155/2023/1969500.

[54] Schwenzer, M., Ay, M., Bergs, T., Abel, D. (2021). “Review on model predictive control: An engineering perspective”. International Journal of Advanced Manufacturing Technology, 117(5-6), 1327-1349,  doi:https://doi.org/10.1007/s00170-021-07682-3.

[55] Shao, K., Zheng, J., Yang, C., Xu, F., Wang, X., Li, X. (2021). “Chattering-free adaptive sliding-mode control of nonlinear systems with unknown disturbances”. Computers & Electrical Engineering, 96(Part A), doi:https://doi.org/10.1016/j.compeleceng.2021.107538.

[56] Su, X., Philip Chen, C.L., Liu, Zh. (2021). “Adaptive fuzzy control for uncertain nonlinear systems subject to full state constraints and actuator faults. Information Sciences, 581, 553-566, doi:https://doi.org/10.1016/j.ins.2021.09.055.

[57] Tong, X., Cheng, S.S. (2023). “Global stabilization of antipodal points on n-sphere with application to attitude tracking”. IEEE Transactions on Automatic Control, 69(2), 1186-1193, doi:https://doi.org/10.1109/TAC.2023.3281341.

[58] Utkin, V.I. (2013). “Sliding modes in control and optimization”. Springer Berlin, Heidelberg, doi:https://doi.org/10.1007/978-3-642-84379-2.

[59] Wang, L.X. (1992). “Fuzzy systems are universal approximators”. [1992 Proceedings] IEEE International Conference on Fuzzy Systems, San Diego, CA, USA, 1163-1170, doi:https://doi.org/10.1109/FUZZY.1992.258721.

[60] Wernecke, H., Sándor, B., Gros, C. (2019). “Chaos in time delay systems, an educational review”. Physics Reports, 824, 1-40, doi:https://doi.org/10.1016/j.physrep.2019.08.001.

[61] Zhang, M., Zang, H., Bai, L. (2022). “A new predefined-time sliding mode control scheme for synchronizing chaotic systems”. Chaos, Solitons & Fractals, 164, doi:https://doi.org/10.1016/j.chaos.2022.112745.

[62] Zhu, E., Xu, M., Pi, D. (2023). “Hopf bifurcation and stability of the double-delay Lorenz system”. International Journal of Bifurcation and Chaos, 33(2), doi:https://doi.org/10.1142. S0218127423500153.

آمار
تعداد مشاهده مقاله: 11
تعداد دریافت فایل اصل مقاله: 3


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب