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Command filter-based I&I adaptive control for MIMO uncertain systems with input saturation and disturbances

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Abstract

This paper develops a control strategy based on immersion and invariance (I&I) adaptive methodology for a class of multi-input multi-output (MIMO) systems in the presence of parametric uncertainty, input saturation, and external disturbance. To avoid the analytic calculation in the backstepping process, a high-gain auxiliary system is constructed to compensate for the effect of command filter error. The first-order command filters are also employed in the construction procedure of the I&I adaptive law to simplify its design and remove the structural conditions on the regressors. A filter-based disturbance observer is developed to counteract the effect of the external disturbance produced by a partially known exogenous system. To overcome the input saturation nonlinearity, a smooth function is introduced to approximate the input saturation with an extended state and a bounding estimation law. Stringent analysis guarantees the stability of closed-loop system. Finally, simulated examples confirm the effectiveness of the suggested method.

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References

  1. Krstic M, Kanellakopoulos I, Kokotovic P V. Nonlinear and Adaptive Control Design. New York: Wiley, 1995

    MATH  Google Scholar 

  2. Astolfi A, Ortega R. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans Automat Contr, 2003, 48: 590–606

    Article  MathSciNet  MATH  Google Scholar 

  3. Karagiannis D, Astolfi A. Nonlinear adaptive control of systems in feedback form: an alternative to adaptive backstepping. Syst Control Lett, 2008, 57: 733–739

    Article  MathSciNet  MATH  Google Scholar 

  4. Karagiannis D, Sassano M, Astolfi A. Dynamic scaling and observer design with application to adaptive control. Automatica, 2009, 45: 2883–2889

    Article  MathSciNet  MATH  Google Scholar 

  5. Ortega R, Hsu L, Astolfi A. Immersion and invariance adaptive control of linear multivariable systems. Syst Control Lett, 2003, 49: 37–47

    Article  MathSciNet  MATH  Google Scholar 

  6. Seo D, Akella M R. Non-certainty equivalent adaptive control for robot manipulator systems. Syst Control Lett, 2009, 58: 304–308

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhao B, Xian B, Zhang Y, et al. Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Trans Ind Electron, 2015, 62: 2891–2902

    Article  Google Scholar 

  8. Zou Y, Meng Z. Immersion and invariance-based adaptive controller for quadrotor systems. IEEE Trans Syst Man Cybern Syst, 2018, 49: 2288–2297

    Article  Google Scholar 

  9. Swaroop D, Hedrick J K, Yip P P, et al. Dynamic surface control for a class of nonlinear systems. IEEE Trans Automat Contr, 2000, 45: 1893–1899

    Article  MathSciNet  MATH  Google Scholar 

  10. Wei Y, Zhou P, Wang Y, et al. Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances. Neurocomputing, 2019, 364: 16–31

    Article  Google Scholar 

  11. Li Y, Li K, Tong S. Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Trans Fuzzy Syst, 2018, 27: 96–110

    Article  Google Scholar 

  12. Liu H, Zhang T, Xia X. Adaptive neural dynamic surface control of MIMO pure-feedback nonlinear systems with output constraints. Neurocomputing, 2019, 333: 101–109

    Article  Google Scholar 

  13. Farrell J A, Polycarpou M, Sharma M, et al. Command filtered backstepping. IEEE Trans Automat Contr, 2009, 54: 1391–1395

    Article  MathSciNet  MATH  Google Scholar 

  14. Dong W J, Farrell J A, Polycarpou M M, et al. Command filtered adaptive backstepping. IEEE Trans Contr Syst Technol, 2012, 20: 566–580

    Article  MATH  Google Scholar 

  15. Cui G, Xu S, Lewis F L, et al. Distributed consensus tracking for non-linear multi-agent systems with input saturation: a command filtered backstepping approach. IET Control Theor Appl, 2016, 10: 509–516

    Article  MathSciNet  Google Scholar 

  16. Zhu G, Du J, Kao Y. Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation. J Franklin Institute, 2018, 355: 7548–7569

    Article  MathSciNet  MATH  Google Scholar 

  17. Homayoun B, Arefi M M, Vafamand N, et al. Neuro-adaptive command filter control of stochastic time-delayed nonstrict-feedback systems with unknown input saturation. J Franklin Institute, 2020, 357: 7456–7482

    Article  MathSciNet  MATH  Google Scholar 

  18. Yu J P, Shi P, Dong W J, et al. Observer and command-filter-based adaptive fuzzy output feedback control of uncertain nonlinear systems. IEEE Trans Ind Electron, 2015, 62: 5962–5970

    Article  Google Scholar 

  19. Yu J P, Shi P, Dong W J, et al. Command filtering-based fuzzy control for nonlinear systems with saturation input. IEEE Trans Cybern, 2016, 47: 2472–2479

    Article  Google Scholar 

  20. Zhao Z, Yu J, Zhao L, et al. Adaptive fuzzy control for induction motors stochastic nonlinear systems with input saturation based on command filtering. Inf Sci, 2018, 463–464: 186–195

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhou J, Wen C. Robust adaptive control of uncertain nonlinear systems in the presence of input saturation. IFAC Proc Volumes, 2006, 39: 149–154

    Article  Google Scholar 

  22. Zhou J, Wen C Y. Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-variations. Berlin: Springer, 2008

    MATH  Google Scholar 

  23. Gao Y F, Sun X M, Wen C, et al. Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Trans Automat Contr, 2016, 62: 2498–2504

    Article  MathSciNet  MATH  Google Scholar 

  24. Hua C, Meng R, Li K, et al. Full state constraints-based adaptive tracking control for uncertain nonlinear stochastic systems with input saturation. J Franklin Institute, 2020, 357: 5125–5142

    Article  MathSciNet  MATH  Google Scholar 

  25. Min H, Xu S, Zhang Z. Adaptive finite-time stabilization of stochastic nonlinear systems subject to full-state constraints and input saturation. IEEE Trans Automat Contr, 2020, 66: 1306–1313

    Article  MathSciNet  MATH  Google Scholar 

  26. Wen C, Zhou J, Liu Z, et al. Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans Automat Contr, 2011, 56: 1672–1678

    Article  MathSciNet  MATH  Google Scholar 

  27. Guo X G, Xu W D, Wang J L, et al. Distributed neuroadaptive fault-tolerant sliding-mode control for 2-D plane vehicular platoon systems with spacing constraints and unknown direction faults. Automatica, 2021, 129: 109675

    Article  MathSciNet  MATH  Google Scholar 

  28. Chen C, Liu Z, Zhang Y, et al. Saturated Nussbaum function based approach for robotic systems with unknown actuator dynamics. IEEE Trans Cybern, 2016, 46: 2311–2322

    Article  Google Scholar 

  29. Wang H, Ren W, Yu W, et al. Fully distributed consensus control for a class of disturbed second-order multi-agent systems with directed networks. Automatica, 2021, 132: 109816

    Article  MathSciNet  MATH  Google Scholar 

  30. Xiao B, Cao L, Ran D. Attitude exponential stabilization control of rigid bodies via disturbance observer. IEEE Trans Syst Man Cybern Syst, 2021, 51: 2751–2759

    Article  Google Scholar 

  31. Yang Y, Li Y, Liu X, et al. Adaptive neural network control for a hydraulic knee exoskeleton with valve deadband and output constraint based on nonlinear disturbance observer. Neurocomputing, 2022, 473: 14–23

    Article  Google Scholar 

  32. Sun T R, Cheng L, Hou Z G, et al. Novel sliding-mode disturbance observer-based tracking control with applications to robot manipulators. Sci China Inf Sci, 2021, 64: 172205

    Article  MathSciNet  Google Scholar 

  33. Cheng X, Liu Z-W, Hou H Z, et al. Disturbance observer-based nonsingular fixed-time sliding mode tracking control for a quadcopter. Sci China Inf Sci, 2022, 65: 192202

    Article  MathSciNet  Google Scholar 

  34. Chen M, Xiong S, Wu Q. Tracking flight control of quadrotor based on disturbance observer. IEEE Trans Syst Man Cybern Syst, 2019, 51: 1414–1423

    Article  Google Scholar 

  35. Kong L, He W, Liu Z, et al. Adaptive tracking control with global performance for output-constrained MIMO nonlinear systems. IEEE Trans Automat Contr, 2023, 68: 3760–3767

    Article  MathSciNet  MATH  Google Scholar 

  36. Yu J P, Shi P, Chen X K, et al. Finite-time command filtered adaptive control for nonlinear systems via immersion and invariance. Sci China Inf Sci, 2021, 64: 192202

    Article  MathSciNet  Google Scholar 

  37. Han C, Liu Z, Yi J. Immersion and invariance adaptive control with σ-modification for uncertain nonlinear systems. J Franklin Institute, 2018, 355: 2091–2111

    Article  MathSciNet  MATH  Google Scholar 

  38. Wang C, Lin Y. Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems. Automatica, 2015, 54: 16–24

    Article  MathSciNet  MATH  Google Scholar 

  39. Wang C, Wen C, Guo L. Decentralized output-feedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures. Automatica, 2016, 71: 187–196

    Article  MathSciNet  MATH  Google Scholar 

  40. Li Y X. Command filter adaptive asymptotic tracking of uncertain nonlinear systems with time-varying parameters and disturbances. IEEE Trans Automat Contr, 2021, 67: 2973–2980

    Article  MathSciNet  MATH  Google Scholar 

  41. Skjetne R, Fossen T I, Kokotović P V. Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory. Automatica, 2005, 41: 289–298

    Article  MathSciNet  MATH  Google Scholar 

  42. He S, Wang M, Dai S L, et al. Leader-follower formation control of USVs with prescribed performance and collision avoidance. IEEE Trans Ind Inf, 2019, 15: 572–581

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by National Key R&D Program of China (Grant No. 2021YFB3301000), National Natural Science Foundation of China (Grant No. 62173297), Zhejiang Key R&D Program (Grant No. 2022C01035), and Fundamental Research Funds for the Central Universities (Grant No. 226-2022-00086).

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Authors and Affiliations

  1. State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, China

    Qi Han, Zhitao Liu, Hongye Su & Xiangbin Liu

  2. School of Electronic Information Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Xiangbin Liu

Authors
  1. Qi Han
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  2. Zhitao Liu
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  3. Hongye Su
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  4. Xiangbin Liu
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Correspondence to Zhitao Liu.

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Han, Q., Liu, Z., Su, H. et al. Command filter-based I&I adaptive control for MIMO uncertain systems with input saturation and disturbances. Sci. China Inf. Sci. 66, 222203 (2023). https://doi.org/10.1007/s11432-022-3770-2

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  • DOI: https://doi.org/10.1007/s11432-022-3770-2

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