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Adaptive Near-Optimal Control Using Sliding Mode

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Deep Reinforcement Learning with Guaranteed Performance

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 265))

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Abstract

In this chapter, an adaptive near-optimal controller, which is inherently real time, is designed to tackle the contradictory between solution accuracy and solution speed for the optimal control of a general class of nonlinear systems with fully unknown parameters. The key technique in the presented adaptive near-optimal control is to design an auxiliary system with the aid of the sliding mode control concept to reconstruct the dynamics of the controlled nonlinear system. Based on the sliding-mode auxiliary system and approximation of the performance index, the presented controller guarantees asymptotic stability of the closed-system and asymptotic optimality of the performance index with time. Two illustrative examples and an application of the presented method to a van der Pol oscillator are presented to validate the efficacy of the presented adaptive near-optimal control. In addition, physical experiment results based on a DC motor are also presented to show the realizability, performance, and superiority of the presented method.

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References

  1. Liu, Y., Tong, S.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016). Feb

    MathSciNet  MATH  Google Scholar 

  2. Lai, G., Chen, C.L.P., Zhang, Y.: Adaptive asymptotic tracking control of uncertain nonlinear system with input quantization. Syst. Control Lett. 96, 23–29 (2016). Oct

    Article  MathSciNet  Google Scholar 

  3. Liu, Y., Gao, Y., Tong, S., Li, Y.: Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone. IEEE Trans. Fuzzy Syst. 24(1), 16–28 (2016). Feb

    Article  Google Scholar 

  4. Liu, Y., Tong, S.: Adaptive fuzzy control for a class of unknown nonlinear dynamical systems. Fuzzy Set. Syst. 263(15), 49–70 (2015). Mar

    Article  MathSciNet  Google Scholar 

  5. Li, S., Chen, S., Liu, B., Li, Y., Liang, Y.: Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks. Neurocomputing 91, 1–10 (2012)

    Google Scholar 

  6. Li, S., Cui, H., Li, Y., Liu, B., Lou, Y.: Decentralized control of collaborative redundant manipulators with partial command coverage via locally connected recurrent neural networks. Neural Comput. Appl. 23(3), 1051–1060 (2013)

    Google Scholar 

  7. Jin, L., Zhang, Y., Li, S., Zhang, Y.: Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans. Ind. Electron. 63(11), 6978–6988 (2016)

    Google Scholar 

  8. Li, S., He, J., Li, Y., Rafique, M.U.: Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 415–426 (2017)

    MathSciNet  Google Scholar 

  9. Jin, L., Li, S., La, H.M., Luo, X.: Manipulability optimization of redundant manipulators using dynamic neural networks. IEEE Trans. Ind. Electron. 64(6), 4710–4720 (2017)

    Google Scholar 

  10. Li, Y., Li, S., Hannaford, B.: A novel recurrent neural network for improving redundant manipulator motion planning completeness. In: ICRA, pp. 2956–2961 (2018)

    Google Scholar 

  11. Zhang, Y., Li, S.: A neural controller for image-based visual servoing of manipulators with physical constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(11), 5419–5429 (2018)

    MathSciNet  Google Scholar 

  12. Li, S., Zhou, M., Luo, X.: Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 4791–4801 (2018)

    MathSciNet  Google Scholar 

  13. Li, S., Wang, H., Rafique, M.U.: A novel recurrent neural network for manipulator control with improved noise tolerance. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1908–1918 (2018)

    MathSciNet  Google Scholar 

  14. Jin, L., Li, S., Luo, X., Li, Y., Qin, B.: Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans. Ind. Inform. 14(9), 3812–3821 (2018)

    Google Scholar 

  15. Li, J., Zhang, Y., Li, S., Mao, M.: New discretization-formula-based zeroing dynamics for real-time tracking control of serial and parallel manipulators. IEEE Trans. Ind. Inf. 14(8), 3416–3425 (2018)

    Article  Google Scholar 

  16. Chen, D., Zhang, Y., Li, S.: Tracking control of robot manipulators with unknown models: a Jacobian-matrix-adaption method. IEEE Trans. Ind. Inf. 14(7), 3044–3053 (2018)

    Article  Google Scholar 

  17. Zhang, Y., Li, S., Gui, J., Luo, X.: Velocity-level control with compliance to acceleration-level constraints: a novel scheme for manipulator redundancy resolution. IEEE Trans. Ind. Inf. 14(3), 921–930 (2018)

    Article  Google Scholar 

  18. Xiao, L., Liao, B., Li, S., Zhang, Z., Ding, L., Jin, L.: Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans. Ind. Inf. 14(1), 98–105 (2018)

    Article  Google Scholar 

  19. Zhang, Y., Chen, S., Li, S., Zhang, Z.: Adaptive projection neural network for kinematic control of redundant manipulators with unknown physical parameters. IEEE Trans. Ind. Electron. 65(6), 4909–4920 (2018)

    Google Scholar 

  20. Zhang, Z., Lin, Y., Li, S., Li, Y., Yu, Z., Luo, Y.: Tricriteria optimization-coordination motion of dual-redundant-robot manipulators for complex path planning. IEEE Trans. Control Syst. Tech. 26(4), 1345–1357 (2018)

    Article  Google Scholar 

  21. Jin, L., Li, S., Hu, B., Yi, C.: Dynamic neural networks aided distributed cooperative control of manipulators capable of different performance indices. Neurocomputing 291, 50–58 (2018)

    Google Scholar 

  22. Jin, L., Li, S., Yu, J., He, J.: Robot manipulator control using neural networks: a survey. Neurocomputing 285, 23–34 (2018)

    Google Scholar 

  23. Chen, D., Zhang, Y., Li, S.: Zeroing neural-dynamics approach and its robust and rapid solution for parallel robot manipulators against superposition of multiple disturbances. Neurocomputing 275, 845–858 (2018)

    Google Scholar 

  24. Li, S., Shao, Z., Guan, Y.: A dynamic neural network approach for efficient control of manipulators. IEEE Trans. Syst. Man Cybern. Syst. 49(5), 932–941 (2019)

    Article  Google Scholar 

  25. Zhang, Y., Li, S., Zhou, X.: Recurrent-neural-network-based velocity-level redundancy resolution for manipulators subject to a joint acceleration limit. IEEE Trans. Ind. Electron. 66(5), 3573–3582 (2019)

    Google Scholar 

  26. Zhang, Z., Chen, S., Li, S.: Compatible convex-nonconvex constrained QP-based dual neural networks for motion planning of redundant robot manipulators. IEEE Trans. Control Syst. Tech. 27(3), 1250–1258 (2019)

    Article  Google Scholar 

  27. Xu, Z., Li, S., Zhou, X., Yan, W., Cheng, T., Huang, D.: Dynamic neural networks based kinematic control for redundant manipulators with model uncertainties. Neurocomputing 329, 255–266 (2019)

    Google Scholar 

  28. Li, S., Zhang, Y., Jin, L.: Kinematic control of redundant manipulators using neural networks. IEEE Trans. Neural Netw. Learn. Syst. (in press)

    Google Scholar 

  29. Mohammed, A.M., Li, S.: Dynamic neural networks for kinematic redundancy resolution of parallel stewart platforms. IEEE Trans. Cybern. 46(7), 1538–1550 (2016). Jul

    Article  Google Scholar 

  30. Jin, L., Zhang, Y.: G2-type SRMPC scheme for synchronous manipulation of two redundant robot Arms. IEEE Trans. Cybern. 45(2), 153–164 (2015). Feb

    Article  Google Scholar 

  31. Jin, L., Li, S., Xiao, L., Lu, R., Liao, B.: Cooperative motion generation in a distributed network of redundant robot manipulators with noises. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1715–1724 (2018)

    Article  Google Scholar 

  32. Jin, L., Li, S.: Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)

    Article  Google Scholar 

  33. Vamvoudakis, K.G.: Q-learning for continuous-time linear systems: a model-free infinite horizon optimal control approach. Syst. Control Lett. 100, 14–20 (2017). Feb

    Article  MathSciNet  Google Scholar 

  34. Lewis, F.L., Vrabie, D., Syrmos, V.L.: Optimal Control. Wiley, Hoboken (2012)

    Book  Google Scholar 

  35. Mayne, D.Q., Michalska, H.: Receding horizon control of nonlinear systems. IEEE Trans. Autom. Control 35(7), 814–824 (1990). Jul

    Article  MathSciNet  Google Scholar 

  36. Johansen, T.A.: Toward dependable embedded model predictive control. IEEE Syst. J. 11(2), 1208–1219 (2017). Jun

    Google Scholar 

  37. Chakrabarty, A., Dinh, V., Corless, M.J., Rundell, A.E., Żack, S.H., Buzzard, G.T.: Support vector machine informed explicit nonlinear model predictive control using low-discrepancy sequences. IEEE Trans. Autom. Control 62(1), 135–148 (2017). Jan

    Article  MathSciNet  Google Scholar 

  38. Chen, W.-H., Ballance, D.J., Gawthrop, P.J.: Optimal control of nonlinear systems: a predictive control approach. Automatica 39(4), 633–641 (2003). Apr

    Article  MathSciNet  Google Scholar 

  39. Zhang, Y., Li, S.: Predictive suboptimal consensus of multiagent systems with nonlinear dynamics. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1701–1711 (2017)

    Article  MathSciNet  Google Scholar 

  40. Zhang, Y., Li, S.: Time-scale expansion-based approximated optimal control for underactuated systems using projection neural networks. IEEE Trans. Syst. Man, Cybern. Syst. 48(11), 1957–1967 (2018)

    Article  Google Scholar 

  41. Yu, Z., Xiao, L., Li, H., Zhu, X., Huai, R.: Model parameter identification for lithium batteries using the coevolutionary particle swarm optimization method. IEEE Trans. Ind. Electron. 64(7), 5690–5700 (2017). Jul

    Article  Google Scholar 

  42. Lee, S.-H., Yoo, A., Lee, H.-J., Yoon, Y.-D., Han, B.-M.: Identification of induction motor parameters at standstill based on integral calculation. IEEE Trans. Ind. Appl. 53(3), 2130–2139 (2017). May

    Article  Google Scholar 

  43. Odhano, S.A., Bojoi, R., Armando, E., Homrich, G., Flores Filho, A.F., Popescu, M., Dorrell, D.G.: Identification of three-phase IPM machine parameters using torque tests. IEEE Trans. Ind. Appl. 53(3), 1883–1891 (2017)

    Article  Google Scholar 

  44. Pin, G., Magni, L., Parisini, T., Raimondo, D.M.: Robust receding - horizon control of nonlinear systems with state dependent uncertainties: an input-to-state stability approach. In: Proceedings of American Control Conference, pp. 1667–1672 (2008)

    Google Scholar 

  45. Zhao, X., Yang, H., Zong, G.: Adaptive neural hierarchical sliding mode control of nonstrict-feedback nonlinear systems and an application to electronic circuits. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1394–1404 (2017)

    Article  Google Scholar 

  46. Yin, S., Yang, H., Kaynak, O.: Sliding mode observer-based FTC for markovian jump systems with actuator and sensor faults. IEEE Trans. Ind. Electron. 62(7), 3551–3558 (2017). Jul

    Google Scholar 

  47. Cao, L., Li, X., Chen, X., Zhao, Y.: Minimum sliding mode error feedback control for fault tolerant small satellite attitude control. Adv. Space Res. 53(2), 309–324 (2014). Jan

    Google Scholar 

  48. Cao, L., Chen, X., Misra, A.K.: Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations. Acta Astronaut. 96, 201–216 (2014). Mar

    Google Scholar 

  49. Isidori, A.: Nonlinear Control Systems: An Introduction, 3rd edn. Springer, New York (1995)

    Book  Google Scholar 

  50. Sun, W., Tang, S., Gao, H., Zhao, J.: Two time-scale tracking control of nonholonomic wheeled mobile robots. IEEE Trans. Control Syst. Technol. 24(6), 2059–2069 (2016). Nov

    Google Scholar 

  51. Baek, J., Jin, M., Han, S.: A new adaptive sliding-mode control scheme for application to robot manipulators. IEEE Trans. Ind. Electron. 63(5), 3632–3637 (2016). Jun

    Google Scholar 

  52. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009). Mar

    Google Scholar 

  53. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998). Mar

    Google Scholar 

  54. Davila, J.: Exact tracking using backstepping control design and high-order sliding modes. IEEE Trans. Autom. Control 58(8), 2077–2081 (2013). Aug

    Article  MathSciNet  Google Scholar 

  55. Chen, C.T.: Linear System Theory and Design. Oxford University Press, New York (1999)

    Google Scholar 

  56. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

  57. Atay, F.M.: Van der Pol’s oscillator under delayed feedback. J. Sound Vib. 218(2), 333–339 (1998)

    Article  MathSciNet  Google Scholar 

  58. Chuang, C.A., Lee, T.T., Tien, C.C., Hsu, C.F.: Adaptive wavelet neural network control for DC motors via second-order sliding-mode approach. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 1174–1179 (2011)

    Google Scholar 

  59. Baek, J., Jin, M., Han, S.: A new adaptive sliding-mode control scheme for application to robot manipulators. IEEE Trans. Ind. Electron. 63(6), 3628–3637 (2016). Jun

    Google Scholar 

  60. Lin, F.-J., Chou, P.-H.: Adaptive control of two-axis motion control system using interval type-2 fuzzy neural network. IEEE Trans. Ind. Electron. 56(1), 178–193 (2009). Jan

    Google Scholar 

  61. Singh, R.K., Yadav, S.: Optimized PI controller for an interacting spherical tank system. In: Proceedings of 1st Conference Electronics Material Engineering Nano-Technology, pp. 1–6 (2017)

    Google Scholar 

  62. Shauri, R.L.A., Salleh, N.M., Hadi, A.K.A.: PID position control of 7-DOF three-fingered robotic hand for grasping task. In: Proceedings of IEEE International Conference on Control System Computing Engineering, pp. 70–74 (2014)

    Google Scholar 

  63. Anantachaisilp, P., Lin, Z.: An experimental study on PID tuning methods for active magnetic bearing systems. Int. J. Adv. Mechatron. Syst. 5(2), 146–154 (2013)

    Article  Google Scholar 

  64. Datasheet. http://www.atmel.com/Images/Atmel-42735-8-bit-AVR-Microcontroller-ATmega328-328P_Datasheet.pdf

  65. Hughes, A., Drury, B.: Electric Motors and Drives: Fundamentals, Types and Applications. Newnes, Oxford (2013)

    Chapter  Google Scholar 

  66. Cao, L., Li, H.: Unscented predictive variable structure filter for satellite attitude estimation with model errors when using low precision sensors. Acta Astronaut. 127, 505–513 (2016). Oct

    Article  Google Scholar 

  67. Cao, L., Chen, Y., Zhang, Z., Li, H.: Predictive smooth variable structure filter for attitude synchronization estimation during satellite formation flying. IEEE Trans. Aerosp. Electron. Syst. 53(3), 1375–1383 (2017). Jun

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Cyber Security, Jinan University, Guangzhou, China

    Yinyan Zhang

  2. School of Information Science and Engineering, Lanzhou University, Lanzhou, China

    Shuai Li

  3. Guangdong Institute of Intelligent Manufacturing, Guangdong Academy of Science, Guangzhou, China

    Xuefeng Zhou

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  1. Yinyan Zhang
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  2. Shuai Li
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  3. Xuefeng Zhou
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Correspondence to Shuai Li .

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Zhang, Y., Li, S., Zhou, X. (2020). Adaptive Near-Optimal Control Using Sliding Mode. In: Deep Reinforcement Learning with Guaranteed Performance. Studies in Systems, Decision and Control, vol 265. Springer, Cham. https://doi.org/10.1007/978-3-030-33384-3_4

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