Abstract
This paper develops a novel adaptive integral sliding-mode control (SMC) technique to improve the tracking performance of a wheeled inverted pendulum (WIP) system, which belongs to a class of continuous time systems with input disturbance and/or unknown parameters. The proposed algorithm is established based on an integrating between the advantage of online adaptive reinforcement learning control and the high robustness of integral sliding-mode control (SMC) law. The main objective is to find a general structure of integral sliding mode control law that can guarantee the system state reaching a sliding surface in finite time. An adaptive/approximate optimal control based on the approximate/adaptive dynamic programming (ADP) is responsible for the asymptotic stability of the closed loop system. Furthermore, the convergence possibility of proposed output feedback optimal control was determined without the convergence of additional state observer. Finally, the theoretical analysis and simulation results validate the performance of the proposed control structure.
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P. N. Dao, V. H. Nguyen, and T. T. Do, “Adaptive dynamic programming based integral sliding mode control law for continuous-time systems: A design for inverted pendulum systems,” International Journal of Mechanical Engineering and Robotics Research, vol. 8, no. 2, pp. 279–283, March 2019.
T. T. Pham, P. N. Dao, V. T. Vu, Q. H. Tran, and V. H. Nguyen, “Robust control law using H-infinity for wheeled inverted pendulum systems,” International Journal of Mechanical Engineering and Robotics Research, vol. 8, no. 3, pp. 483–487, May 2019.
R. Cui, G. Ji, and M. Zhaoyong, “Adaptive backstepping control of wheeled inverted pendulums models,” Nonlinear Dynamics, vol. 79, no. 1, pp. 501–511, 2015.
Z. Li and J. Luo, “Adaptive robust dynamic balance and motion controls of mobile wheeled inverted pendulums,” IEEE Transactions on Control Systems Technology, vol. 17, no. 1, pp. 233–241, 2008.
Z. Li and Y. Zhang, “Robust adaptive motion/force control for wheeled inverted pendulums,” Automatica, vol. 46, no. 8, pp. 1346–1353, 2010.
Z. Li, “Adaptive fuzzy output feedback motion/force control for wheeled inverted pendulums,” IET Control Theory & Applications, vol. 5, no. 10, pp. 1176–1188, 2011.
J. Kumar, V. Kumar, and K. P. S. Rana, “Design of robust fractional order fuzzy sliding mode PID controller for two link robotic manipulator system,” Journal of Intelligent & Fuzzy Systems, vol. 35, no. 5, pp. 5301–5315, 2018.
J. de J. Rubio, J. Pieper, J. A. Meda-Campaña, A. Aguilar, V. I. Rangel, and G. J. Gutierrez, “Modelling and regulation of two mechanical systems,” IET Science, Measurement & Technology, vol. 12, no. 5, pp. 657–665, 2018.
Z. Li and C. Yang, “Neural-adaptive output feedback control of a class of transportation vehicles based on wheeled inverted pendulum models,” IEEE Transactions on Control Systems Technology, vol. 20, no. 6, pp. 1583–1591, 2012.
J. de J. Rubio, “Robust feedback linearization for nonlinear processes control,” ISA Transactions, vol. 74, pp. 155–164, 2018.
J. de J. Rubio, G. Ochoa, D. Mujica-Vargas, E. Garcia, E. Balcazar, Ricardo, I. Elias, D. R. Cruz, and C. F. Juarez, A. Aguilar, and J. F. Novoa, “Structure regulator for the perturbations attenuation in a quadrotor,” IEEE Access, vol. 7, pp. 138244–138252, 2019.
C. Yang, Z. Li, and J. Li, “Trajectory planning and optimized adaptive control for a class of wheeled inverted pendulum vehicle models,” IEEE Transactions on Cybernetics, vol. 17, no. 1, pp. 233–241, 2008.
H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 2002.
C. Yang, Z. Li, R. Cui, and B. Xu, “Neural network-based motion control of an underactuated wheeled inverted pendulum model,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, issue. 11, pp. 2004–2016, 2014.
M. Yue, X. Wei, and Z. Li, “Adaptive sliding-mode control for two-wheeled inverted pendulum vehicle based on zero-dynamics theory,” Nonlinear Dynamics, vol. 76, issue. 1, pp. 459–471, 2014.
K. Sun, S. Mou, J. Qiu, T. Wang, and H. Gao, “Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 8, pp. 1587–1601, 2018.
J. Qiu, K. Sun, I. J. Rudas, and H. Gao, “Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis,” IEEE Transactions on Cybernetics, vol. 50, no. 7, pp. 2905–2915, 2019.
Z. Q. Guo, J. X. Xu, T. H. Lee, “Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum,” Journal of the Franklin Institute, vol. 351, issue. 4, pp. 2261–2282, 2014.
K. Y. Chen, “Robust optimal adaptive sliding mode control with the disturbance observer for a manipulator robot system,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1701–1715, 2018.
Y. Lv, X. Ren, S. Hu, H. Xu, “Approximate optimal stabilization control of servo mechanisms based on reinforcement learning scheme,” International Journal of Control, Automation and Systems, vol. 17, no. 10, pp. 2655–2665, 2019.
X. Yang, D. Liu, B. Luo, and C. Li, “Data-based robust adaptive control for a class of unknown nonlinear constrained-input systems via integral reinforcement learning,” Information Sciences, vol. 369, pp. 736–747, 2016.
D. Vrabie, O. Pastravanu, M. Abu. Khalaf, and F. L. Lewis, “Adaptive optimal control for continuous-time linear systems based on policy iteration,” Automatica, vol. 45, no. 2, pp. 477–484, 2009.
Y. Jiang and Z. P. Jiang, “Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics,” Automatica, vol. 48, no. 10, pp. 2699–2704, 2012.
D. Vrabie and F. Lewis, “Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systems,” Neural Networks, vol. 22, no. 3, pp. 237–246, 2009.
M. A. Khalaf and F. L. Lewis, “Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach,” Automatica, vol. 41, no. 5, pp. 779–791, 2005.
K. G. Vamvoudakis and F. L. Lewis, “Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem,” Automatica, vol. 46, no. 5, pp. 878–888, 2010.
K. G. Vamvoudakis, D. Vrabie, and F. L. Lewis, “Online adaptive algorithm for optimal control with integral reinforcement learning,” International Journal of Robust and Nonlinear Control, vol. 24, issue. 17, pp. 2686–2710, 2014.
S. Bhasin, R. Kamalapurkar, M. Johnson, K. G. Vamvoudakis, F. L. Lewis, and W. E. Dixon, “A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems,” Automatica, vol. 49, issue. 1, pp. 82–92, 2013.
B. Kiumarsi, F. L. Lewis, and Z. P. Jiang, “H∞ control of linear discrete-time systems: Off-policy reinforcement learning,” Automatica, vol. 78, pp. 148–152, 2017.
X. Zhang, H. Zhang, Q. Sun, and Y. Luo, “Adaptive dynamic programming-based optimal control of unknown nonaffine nonlinear discrete-time systems with proof of convergence,” Neurocomputing, vol. 91, pp. 48–55, 2012.
W. Gao and Z. P. Jiang, “Adaptive optimal output regulation via output-feedback: An adaptive dynamic programing approach,” Proc. of 2016 IEEE 55th Conference on Decision and Control (CDC), pp. 5845–5850, 2016.
J. Li and Q. Zhang, “Fuzzy reduced-order compensator-based stabilization for interconnected descriptor systems via integral sliding modes,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 4, pp. 752–765, 2017.
A. A. Bature, S. Buyamin, M. N. Ahmad, and M. Muhammad, “A comparison of controllers for balancing two wheeled inverted pendulum robot,” International Journal of Mechanical & Mechatronics Engineering, vol. 14, no. 3, pp. 62–68, 2014.
J. Liu, Y. Gao, X. Su, M. Wack, and L. Wu, “Disturbance-observer-based control for air management of PEM fuel cell systems via sliding mode technique,” IEEE Transactions on Control Systems Technology, vol. 27, no. 3, pp. 1129–1138, 2018.
Y. Gao, J. Liu, Z. Wang, and L. Wu, “Interval type-2 FNN-based quantized tracking control for hypersonic flight vehicles with prescribed performance,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2911726
Y. Gao, J. Liu, G. Sun, M. Liu, and L. Wu, “Fault deviation estimation and integral sliding mode control design for Lipschitz nonlinear systems,” Systems & Control Letters, vol. 123, pp. 8–15, 2019.
S. Mobayen, “Adaptive global terminal sliding mode control scheme with improved dynamic surface for uncertain nonlinear systems,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1692–1700, 2018.
J. Li and Q. Zhang, “A linear switching function approach to sliding mode control and observation of descriptor systems,” Automatica, vol. 95, pp. 112–121, 2018.
J. Li and G. Yang, “Fuzzy descriptor sliding mode observer design: A canonical form-based method,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 9, pp. 2048–2062, 2020.
D. Kleinman, “On an iterative technique for Riccati equation computations,” IEEE Transactions on Automatic Control, vol. 13, no. 1, pp. 114–115, 1968.
C. Mu and D. Wang, “Neural-network-based adaptive guaranteed cost control of nonlinear dynamical systems with matched uncertainties,” Neurocomputing, vol. 245, pp. 46–54, 2017.
F. Castaños and L. Fridman, “Analysis and design of integral sliding manifolds for systems with unmatched perturbations,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 853–858, 2006.
X. Yang, D. Liu, B. Luo, and C. Li, “Data-based robust adaptive control for a class of unknown nonlinear constrained-input systems via integral reinforcement learning,” Information Sciences, vol. 369, pp. 731–747, 2016.
Y. Jiang and Z. Jiang, Robust Adaptive Dynamic Programming, John Wiley & Sons, 2017.
H. Modares, F. L. Lewis, and M.-B. Naghibi-Sistani, “Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems,” Automatica, vol. 50, no.1, pp. 193–202, 2014.
K. G. Vamvoudakis, M. F. Miranda, and J. P. Hespanha, “Asymptotically stable adaptive-optimal control algorithm with saturating actuators and relaxed persistence of excitation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no.11, pp. 2386–2398, 2015.
D. Xu, Q. Wang, and Y. Li, “Optimal guaranteed cost tracking of uncertain nonlinear systems using adaptive dynamic programming with concurrent learning,” International Journal of Control, Automation and Systems, vol. 18, no.5, pp. 1116–1127, 2020.
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Recommended by Editor Jessie (Ju H.) Park. This work was supported in part by the Ministry of Science and Technology (MOST), Taiwan, under grant MOST 108-2636-E-006-007 and MOST 109-2636-E-006-019 (Young Scholar Fellowship Program).
Phuong Nam Dao received his Ph.D. degree in electrical engineering from Hanoi University of Science and Technology, Hanoi, Vietnam in 2013. Currently, he holds the position as a lecturer at Hanoi University of Science and Technology, Vietnam. His research interests include control of robotic systems and robust/adaptive, optimal control.
Yen-Chen Liu received his B.S. and M.S. degrees in mechanical engineering from National Chiao Tung University, Hsinchu, Taiwan, in 2003 and 2005, respectively, and a Ph.D. degree in mechanical engineering from the University of Maryland, College Park, MD, USA, in 2012. He is currently an Associate Professor with the Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan. His research interests include control of networked robotic systems, bilateral teleoperation, multi-robot systems, semiautonomous systems, and human-robot interaction. He received the MOST Ta-You Wu Memorial Award in 2016, Kwoh-Ting Li Researcher Award by National Cheng Kung University, Taiwan in 2018, and MOST Young Scholar Fellowship in 2019.
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Dao, P.N., Liu, YC. Adaptive Reinforcement Learning Strategy with Sliding Mode Control for Unknown and Disturbed Wheeled Inverted Pendulum. Int. J. Control Autom. Syst. 19, 1139–1150 (2021). https://doi.org/10.1007/s12555-019-0912-9
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DOI: https://doi.org/10.1007/s12555-019-0912-9