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Articles

Pareto Optimal Design of a Fuzzy Adaptive Hierarchical Sliding-mode Controller for an X-Z Inverted Pendulum System

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REFERENCES

  • K. Chakraborty, R. R. Mukherjee, and S. Mukherjee, “Tuning of PID controller of inverted pendulum using genetic algorithm,” Int. J. Soft Comput. Eng., Vol. 3, no. 1, pp. 21–24, Mar. 2013.
  • S. K. Mishra, and D. Chandra, “Stabilization and tracking control of inverted pendulum using fractional order PID controllers,” J. Eng., Vol. 2014, pp. 1–9, Apr. 2014.
  • S. Riachy, Y. Orlov, T. Floquet, R. Santiesteban, and J. P. Richard, “Second-order sliding mode control of underactuated mechanical systems I: local stabilization with application to an inverted pendulum,” Int. J. Robust Nonlinear Control, Vol. 18, no. 4-5, pp. 529–543, Mar. 2008.
  • M. Yue, X. Wei, and Z. Li, “Adaptive sliding-mode control for two-wheeled inverted pendulum vehicle based on zero-dynamics theory,” Nonlinear Dyn., Vol. 76, pp. 459–471, Apr. 2014.
  • D. Qian, J. Yi, D. Zhao, and Y. Hao, “Hierarchical sliding mode control for series doubled inverted pendulum system,” in International Conference on Intelligent Robots and Systems, Beijing, China, 9–15 Oct. 2006, pp. 4977–4982.
  • M. J. Mahmoodabadi, A. Bagheri, N. Nariman-zadeh, A. Jamali, and R. Abedzadeh Maafi, “Pareto design of decoupled sliding-mode controllers for nonlinear systems based on a multiobjective genetic algorithm,” J. Appl. Math., Vol. 2012, pp. 1–22, Aug. 2012.
  • M. J. Mahmoodabadi, R. Abedzadeh Maafi, S. Etemadi Haghighi, and A. Moradi, “Pareto design of decoupled fuzzy sliding mode controller for nonlinear and underactuated systems using a hybrid optimization algorithm,” South Afr. Res. J., Vol. 111, no. 1, pp. 4–21, Mar. 2020.
  • L. C. Hung, and H. Y. Chung, “Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems,” Int. J. Approx. Reason., Vol. 46, no. 1, pp. 74–97, Sep. 2007.
  • D. Ashtiani Haghighi, and S. Mobayen, “Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems,” ISA Trans., Vol. 75, pp. 216–225, Apr. 2018.
  • M. J. Mahmoodabadi, and H. Khoobroo Haghbayan, “An optimal adaptive hybrid controller for a fourth-order under-actuated nonlinear inverted pendulum system,” Trans. Inst. Meas. Control, Vol. 42, no. 2, pp. 285–294, 2020.
  • J. Yi, and N. Yubazaki, “Stabilization fuzzy control of inverted pendulum systems,” Artif. Intell. Eng., Vol. 14, no. 2, pp. 153–163, Apr. 2000.
  • M. I. El-Hawwary, A. L. Elshafei, H. M. Emara, and H. A. A. Fattah, “Adaptive fuzzy control of the inverted pendulum problem,”,” IEEE Trans. Control Syst. Technol., Vol. 14, no. 6, pp. 1135–1144, Nov. 2006.
  • A. Ebrahim, and G. V. Murphy, “Adaptive backstepping controller design of an inverted pendulum,” in Proceedings of the Thirty-Seventh Southeastern Symposium on System Theory, Tuskegee, AL, 20–22 Mar. 2005, pp. 172–174.
  • A. K. Patra, S. S. Biswal, and P. K. Rout, “Backstepping linear quadratic Gaussian controller design for balancing an inverted pendulum,” IETE. J. Res., 1–15, Mar. 2019.
  • D. Maravall, “Control and stabilization of the inverted pendulum via vertical forces,” in Robotic welding, Intelligence and automation, Lecture Notes in Control and Information Sciences, Vol. 299, T. J. Tarn, C. Zhou, and S. B. Chen, Eds. Berlin: Springer-Verlag, May 2004, pp. 190–211.
  • D. Maravall, C. Zhou, and J. Alonso, “Hybrid fuzzy control of the inverted pendulum via vertical forces,” Int. J. Intell. Syst., Vol. 20, no. 2, pp. 195–211, Feb. 2005.
  • M. Kanazawa, S. Nakaura, and M. Sampei, “Inverse optimal control problem for bilinear systems: application to the inverted pendulum with horizontal and vertical movement,” in Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, Shanghai, China, 15–18 Dec. 2009, pp. 2260–2267.
  • J. J. Wang, “Simulation studies of inverted pendulum based on PID controllers,” Simul. Model. Pract. Theory, Vol. 19, no. 1, pp. 440–449, Jan. 2011.
  • J. J. Wang, “Stabilization and tracking control of X-Z inverted pendulum with sliding-mode control,” ISA Trans., Vol. 51, no. 6, pp. 763–770, Nov. 2012.
  • J. J. Wang, and T. Kumbasar, “Big bang-big crunch optimized hierarchical sliding-mode control of X-Z inverted pendulum,” Simul. Model. Pract. Theory., Vol. 86, pp. 25–35, Aug. 2018.
  • H. Ouyang, J. Wang, G. Zhang, L. Mei, and X. Deng, “Novel adaptive hierarchical sliding mode control for trajectory tracking and load sway rejection in double-pendulum overhead cranes,” IEEE. Access., Vol. 7, pp. 10353–10361, Jan. 2019.
  • M. Van, M. Mavrovouniotis, and S. S. Ge, “An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators,” IEEE Trans. Syst. Man Cybern. Syst., Vol. 49, no. 7, pp. 1448–1458, Jul. 2019.
  • M. J. Mahmoodabadi, and M. M. Shahangin, “A new multi-objective artificial bee colony algorithm for optimal adaptive robust controller design,” IETE. J. Res., 1–14, Jul. 2019.
  • T. Huang, D. Huang, Z. Wang, and A. Shah, “Robust tracking control of a quadrotor UAV based on adaptive sliding mode controller,” Complexity, Vol. 2019, pp. 1–15, Dec. 2019.
  • W. Sun, S. F. Su, J. Xia, and Y. Wu, “Adaptive tracking control of wheeled inverted pendulums with periodic disturbances,” IEEE Trans. Cybern., Vol. 50, no. 5, pp. 1867–1876, May 2020.
  • L. A. Zadeh, “Fuzzy sets,” Inf. Control, Vol. 8, no. 3, pp. 338–353, 1965.
  • R.-C. Roman, R.-E. Precup, and R.-C. David, “Second order intelligent proportional-integral fuzzy control of twin rotor aerodynamic systems,” Procedia. Comput. Sci., Vol. 139, pp. 372–380, Oct. 2018.
  • Z. Zhu, Y. Pan, Q. Zhou, and C. Lu, “Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmetered states and unknown backlash-like hysteresis,” IEEE Trans. Fuzzy Syst., 1–19, Feb. 2020.
  • M. Zare, F. Pazooki, and S. Etemadi Haghighi, “Quadrotor UAV position and altitude tracking using an optimized fuzzy-sliding mode control,” IETE. J. Res., 1–15, Jul. 2020.
  • R.-C. Roman, R.-E. Precup, and E. M. Petriu, “Hybrid data-driven fuzzy active disturbance rejection control for tower crane systems,” Eur. J. Control, Vol. 58, pp. 373–387, Mar. 2021.
  • M. J. Mahmoodabadi, M. Taherkhorsandi, R. A. Maafi, and K. K. Castillo-Villar, “A novel multi-objective optimization algorithm: artificial bee colony in conjunction with bacterial foraging,” Int. J. Intell. Eng. Inform., Vol. 3, no. 4, pp. 369–386, Nov. 2015.
  • S. Z. Zhao, M. Willjuice Iruthayarajan, S. Baskar, and P. N. Suganthan, “Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization,” Inf. Sci., Vol. 181, no. 16, pp. 3323–3335, Aug. 2011.
  • H. V. Hultmann Ayala, and L. dos Santos Coelho, “Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator,” Expert. Syst. Appl., Vol. 39, no. 10, pp. 8968–8974, Aug. 2012.
  • M. J. Mahmoodabadi, A. Bagheri, R. Abedzadeh Maafi, and G. R. Hosseini, “Pareto optimal design of square cyclone separators using a novel multi-objective optimization algorithm,” Trans. Inst. Meas. Control, Vol. 35, no. 3, pp. 289–300, May 2013.
  • J. Luo, Y. Qi, J. Xie, and X. Zhang, “A hybrid multi-objective PSO-EDA algorithm for reservoir flood control operation,” Appl. Soft. Comput., Vol. 34, pp. 526–538, Sep. 2015.
  • B. S. Chen, and S. J. Ho, “Multiobjective tracking control design of T-S fuzzy systems: fuzzy Pareto optimal approach,” Fuzzy Sets Syst., Vol. 290, pp. 39–55, May 2016.
  • E. Nikmanesh, O. Hariri, H. Shams, and M. Fasihozaman, “Pareto design of load frequency control for interconnected power systems based on multi-objective uniform diversity genetic algorithm (MUGA),” Int. J. Electr. Power Energy Syst., Vol. 80, pp. 333–346, Sep. 2016.
  • M. G. Villarreal-Cervantes, “Approximate and widespread Pareto solutions in the structure-control design of mechatronic systems,” J. Optim. Theory. Appl., Vol. 173, pp. 628–657, May 2017.
  • M. Demirtas, E. Ilten, and H. Calgan, “Pareto-based multi-objective optimization for fractional order PIλ speed control of induction motor by using Elman neural network,” Arab. J. Sci. Eng., Vol. 44, pp. 2165–2175, Mar. 2019.
  • M. J. Mahmoodabadi, and N. R. Babak, “Fuzzy adaptive robust proportional–integral–derivative control optimized by the multi-objective grasshopper optimization algorithm for a nonlinear quadrotor,” J. Vib. Con., Vol 26, no. 17–18, pp. 1574–1589, Sep. 2020.
  • X. Jiang, S. Tian, T. Zhang, and W. Zhang, “Pareto optimal strategy for linear stochastic systems with H∞ constraint in finite horizon,” Inf. Sci., Vol. 512, pp. 1103–1117, Feb. 2020.
  • M. J. Mahmoodabadi, R. Abedzadeh Maafi, and M. Taherkhorsandi, “An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems,” Appl. Soft. Comput., Vol. 52, pp. 1191–1199, Mar. 2017.
  • K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput., Vol. 6, no. 2, pp. 182–197, Apr. 2002.

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