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Fully actuated system approaches for continuous-time delay systems: part 2. Systems with input delays

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Abstract

In this paper, the fully actuated system (FAS) approaches for continuous-time systems with time-varying state delays and a constant input delay are presented. Two types of continuous-time high-order FASs are proposed: single-order FASs with both state and input delays and multi-order FASs with both state and input delays. Controllers for both types of time-delay FASs are designed based on the full-actuation features of the systems. Unlike the case of FASs with state delays only, a prediction scheme is required and constructed for both types of FASs with input delays. Similar to the case of FASs with state delays only, constant linear closed-loop systems with arbitrarily assignable eigenstructures are also developed. Illustrative examples are provided to demonstrate the effect of the proposed theories.

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References

  1. Gu K, Niculescu S I. Survey on recent results in the stability and control of time-delay systems. J Dyn Syst Meas Control, 2003, 125: 158–165

    Article  Google Scholar 

  2. Richard J P. Time-delay systems: an overview of some recent advances and open problems. Automatica, 2003, 39: 1667–1694

    Article  MathSciNet  Google Scholar 

  3. Niculescu S I. Delay Effects on Stability: A Robust Control Approach. Berlin: Springer, 2001

    Google Scholar 

  4. Smith O J M. Closer control of loops with dead time. Chem Eng Prog, 1957, 53: 217–219

    Google Scholar 

  5. Smith O J M. A controller to overcome dead time. ISA J, 1959, 6: 28–33

    Google Scholar 

  6. Manitius A Z, Olbrot A W. Finite spectrum assignment problem for systems with delays. IEEE Trans Automat Contr, 1979, 24: 541–552

    Article  MathSciNet  Google Scholar 

  7. Kwon W, Pearson A. Feedback stabilization of linear systems with delayed control. IEEE Trans Automat Contr, 1980, 25: 266–269

    Article  MathSciNet  Google Scholar 

  8. Pekar L, Gao Q. Spectrum analysis of LTI continuous-time systems with constant delays: a literature overview of some recent results. IEEE Access, 2018, 6: 35457–35491

    Article  Google Scholar 

  9. Bekiaris-Liberis N, Krstic M. Compensation of state-dependent input delay for nonlinear systems. IEEE Trans Automat Contr, 2012, 58: 275–289

    Article  MathSciNet  Google Scholar 

  10. Krstic M. Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans Autom Control, 2009, 55: 287–303

    Article  MathSciNet  Google Scholar 

  11. Krstic M. On compensating long actuator delays in nonlinear control. IEEE Trans Automat Contr, 2008, 53: 1684–1688

    Article  MathSciNet  Google Scholar 

  12. Mazenc F, Mondie S, Francisco R. Global asymptotic stabilization of feedforward systems with delay in the input. IEEE Trans Automat Contr, 2004, 49: 844–850

    Article  MathSciNet  Google Scholar 

  13. Mazenc F, Bliman P A. Backstepping design for time-delay nonlinear systems. IEEE Trans Automat Contr, 2006, 51: 149–154

    Article  MathSciNet  Google Scholar 

  14. Mazenc F, Niculescu S I. Generating positive and stable solutions through delayed state feedback. Automatica, 2011, 47: 525–533

    Article  MathSciNet  Google Scholar 

  15. Mazenc F, Niculescu S I, Krstic M. Lyapunov-Krasovskii functionals and application to input delay compensation for linear time-invariant systems. Automatica, 2012, 48: 1317–1323

    Article  MathSciNet  Google Scholar 

  16. Karafyllis I, Pepe P, Jiang Z P. Stability results for systems described by coupled retarded functional differential equations and functional difference equations. Nonlinear Anal-Theor Methods Appl, 2009, 71: 3339–3362

    Article  MathSciNet  Google Scholar 

  17. Kamalapurkar R, Fischer N, Obuz S, et al. Time-varying input and state delay compensation for uncertain nonlinear systems. IEEE Trans Automat Contr, 2015, 61: 834–839

    Article  MathSciNet  Google Scholar 

  18. Pepe P, Karafyllis I, Jiang Z P. On the Liapunov-Krasovskii methodology for the ISS of systems described by coupled delay differential and difference equations. Automatica, 2008, 44: 2266–2273

    Article  MathSciNet  Google Scholar 

  19. Teel A R. Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE Trans Automat Contr, 1998, 43: 960–964

    Article  MathSciNet  Google Scholar 

  20. Sun J, Chen J. A survey on Lyapunov-based methods for stability of linear time-delay systems. Front Comput Sci, 2017, 11: 555–567

    Article  Google Scholar 

  21. Zhang X M, Han Q L, Seuret A, et al. Overview of recent advances in stability of linear systems with time-varying delays. IET Control Theor Appl, 2019, 13: 1–16

    Article  MathSciNet  Google Scholar 

  22. Nihtilä M T. Adaptive control of a continuous-time system with time-varying input delay. Syst Control Lett, 1989, 12: 357–364

    Article  MathSciNet  Google Scholar 

  23. Nihtila M. Finite pole assignment for systems with time-varying input delays. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, 1991. 927–928

  24. Krstic M. Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Trans Automat Contr, 2010, 55: 554–559

    Article  MathSciNet  Google Scholar 

  25. Zhou B. Pseudo-predictor feedback stabilization of linear systems with time-varying input delays. Automatica, 2014, 50: 2861–2871

    Article  MathSciNet  Google Scholar 

  26. Bekiaris-Liberis N, Krstic M. Compensation of time-varying input and state delays for nonlinear systems. J Dynamic Syst Measurement Control, 2011, 134: 011009

    Article  Google Scholar 

  27. Obuz S, Klotz J R, Kamalapurkar R, et al. Unknown time-varying input delay compensation for uncertain nonlinear systems. Automatica, 2017, 76: 222–229

    Article  MathSciNet  Google Scholar 

  28. Duan G R. High-order system approaches: I. Full-actuation and parametric design (in Chinese). Acta Autom Sin, 2020, 46: 1333–1345

    Google Scholar 

  29. Duan G R. High-order system approaches: II. Controllability and fully-actuation (in Chinese). Acta Autom Sin, 2020, 46: 1571–1581

    Google Scholar 

  30. Duan G R. High-order system approaches: III. Observability and observer design (in Chinese). Acta Autom Sin, 2020, 46: 1885–1895

    Google Scholar 

  31. Duan G R. High-order fully actuated system approaches: part I. Models and basic procedure. Int J Syst Sci, 2021, 52: 422–435

    Article  MathSciNet  Google Scholar 

  32. Duan G R. High-order fully actuated system approaches: part II. Generalized strict-feedback systems. Int J Syst Sci, 2021, 52: 437–454

    Article  MathSciNet  Google Scholar 

  33. Duan G R. High-order fully actuated system approaches: part III. Robust control and high-order backstepping. Int J Syst Sci, 2021, 52: 952–971

    Article  MathSciNet  Google Scholar 

  34. Duan G R. High-order fully actuated system approaches: part IV. Adaptive control and high-order backstepping. Int J Syst Sci, 2021, 52: 972–989

    Article  MathSciNet  Google Scholar 

  35. Duan G R. High-order fully actuated system approaches: part V. Robust adaptive control. Int J Syst Sci, 2021, 52: 2129–2143

    Article  MathSciNet  Google Scholar 

  36. Duan G R. High-order fully-actuated system approaches: part VI. Disturbance attenuation and decoupling. Int J Syst Sci, 2021, 52: 2161–2181

    Article  MathSciNet  Google Scholar 

  37. Duan G R. High-order fully actuated system approaches: part VII. Controllability, stabilisability and parametric designs. Int J Syst Sci, 2021, 52: 3091–3114

    Article  MathSciNet  Google Scholar 

  38. Duan G R. High-order fully actuated system approaches: part VIII. Optimal control with application in spacecraft attitude stabilisation. Int J Syst Sci, 2022, 53: 54–73

    Article  MathSciNet  Google Scholar 

  39. Duan G R. High-order fully-actuated system approaches: part IX. Generalised PID control and model reference tracking. Int J Syst Sci, 2022, 53: 652–674

    Article  MathSciNet  Google Scholar 

  40. Duan G R. High-order fully actuated system approaches: part X. Basics of discrete-time systems. Int J Syst Sci, 2022, 53: 810–832

    Article  MathSciNet  Google Scholar 

  41. Duan G R, Zhou B. Fully actuated system approach for linear systems control: a frequency-domain solution. J Syst Sci Complex, 2022, 35: 2046–2061

    Article  MathSciNet  Google Scholar 

  42. Duan G R. Discrete-time delay systems: part 1. Global fully actuated case. Sci China Inf Sci, 2022, 65: 182201

    Article  MathSciNet  Google Scholar 

  43. Duan G R. Discrete-time delay systems: part 2. Sub-fully actuated case. Sci China Inf Sci, 2022, 65: 192201

    Article  MathSciNet  Google Scholar 

  44. Duan G R. Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only. Sci China Inf Sci, 2023, 66: 112201

    Article  MathSciNet  Google Scholar 

  45. Battilotti S. Continuous-time and sampled-data stabilizers for nonlinear systems with input and measurement delays. IEEE Trans Automat Contr, 2020, 65: 1568–1583

    Article  MathSciNet  Google Scholar 

  46. Duan G R. Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems. IEEE Trans Automat Contr, 1993, 38: 276–280

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work has been partially supported by Major Program of National Natural Science Foundation of China (Grant Nos. 61690210, 61690212), National Natural Science Foundation of China (Grant No. 61333003), and Science Center Program of the National Natural Science Foundation of China (Grant No. 62188101). The author is grateful to his Ph.D. students Guangtai TIAN, Qin ZHAO, Weizhen LIU, Hong JIANG, Xiubo WANG, Liyao HU, Kaixin CUI, etc., for helping him with reference selection and proofreading. His particular thanks go to Prof. Bin ZHOU for his helpful comments, and his student Tianyi ZHAO for help with the example simulations.

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Authors and Affiliations

  1. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen, 518055, China

    Guangren Duan

  2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Guangren Duan

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  1. Guangren Duan
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Correspondence to Guangren Duan.

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Duan, G. Fully actuated system approaches for continuous-time delay systems: part 2. Systems with input delays. Sci. China Inf. Sci. 66, 122201 (2023). https://doi.org/10.1007/s11432-021-3460-y

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