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Control of Dynamic Systems under Input and Output Constraints

  • NONLINEAR SYSTEMS
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Abstract

This paper extends the method originally proposed in [1] to systems with an arbitrary number of inputs and outputs. The method ensures that these signals will be in given domains. Two sequential changes of coordinates are introduced to solve the problem. The first change reduces the plant’s output to a new variable of a dimension not exceeding that of the control vector (input). The second change allows passing from the control problem with constraints to the one without them. The effectiveness of this method is illustrated for two problems. The first problem is designing a state-feedback controller for linear systems with constraints imposed on the input and state variables. The second problem is designing an output-feedback controller for linear systems with constraints imposed on the output and input. In both problems, the stability of the closed loop system is verified in terms of linear matrix inequalities. The results are accompanied by simulation examples to show the effectiveness of the proposed method.

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REFERENCES

  1. Furtat, I.B. and Gushchin, P.A., Control of Dynamical Plants with a Guarantee for the Controlled Signal to Stay in a Given Set, Autom. Remote Control, 2021, vol. 82, no. 4, pp. 654–669.

    Article  MathSciNet  MATH  Google Scholar 

  2. Furtat, I. and Gushchin, P., Nonlinear Feedback Control Providing Plant Output in Given Set, Int. J. Control, 2022, vol. 95, no. 6, pp. 1533–1542. https://doi.org/10.1080/00207179.2020.1861336

    Article  MathSciNet  MATH  Google Scholar 

  3. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nonlinear and Adaptive Control of Complex Systems, Dordrecht–Boston–London: Kluwer Academic Publishers, 1999.

    MATH  Google Scholar 

  4. Spong, M., Corke, P., and Lozano, R., Nonlinear Control of the Reaction Wheel Pendulum, Automatica, 2001, vol. 37, pp. 1845–1851.

    Article  MATH  Google Scholar 

  5. Sun, W., Su, S.F., Xia, J., and Wu, Y., Adaptive Tracking Control of  Wheeled Inverted Pendulums with Periodic Disturbances, IEEE Trans. Cybernetics, 2020, vol. 50, no. 5, pp. 1867–1876.

    Article  Google Scholar 

  6. Saleem, O. and Mahmood-ul-Hasan, K., Adaptive State-space Control of Under-actuated Systems Using Error-magnitude Dependent Self-tuning of Cost Weighting-factors, Int. J. Control Automat. Syst., 2021, vol. 19, pp. 931–941.

    Article  Google Scholar 

  7. Khalil, H.K., Nonlinear Systems, 3rd ed., Pearson, 2001.

    Google Scholar 

  8. Demyanov, V.F. and Rubinov, A.M., Introduction to Constructive Nonsmooth Analysis, Frankfurt am Main: Peter Lang Verlag, 1995.

  9. Dolgopolik, M.V. and Fradkov, A.L., Nonsmooth and Discontinuous Speed-Gradient Algorithms, Nonlinear Anal. Hybrid Syst., 2017, vol. 25, pp. 99–113.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yakubovich, V., S-procedure in Nonlinear Control Theory, Vestn. Leningr. Univ., 1971, no. 1, pp. 62–77.

  11. Polyak, B.T., Convexity of Quadratic Transformations and Its Use in Control and Optimization, J. Optim. Theory Appl., 1998, vol. 99, pp. 553–583.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gusev, S.V. and Likhtarnikov, A.L., Kalman–Popov–Yakubovich Lemma and the S-procedure: A Historical Essay, Autom. Remote Control, 2006, vol. 67, no. 11, pp. 1768–1810.

    Article  MathSciNet  MATH  Google Scholar 

  13. Fridman, E., A Refined Input Delay Approach to Sampled-Data Control, Automatica, 2010, vol. 46, pp. 421–427.

    Article  MathSciNet  MATH  Google Scholar 

  14. Polyak, B.T., Khlebnikov, M.V, and Shcherbakov, P.S., Upravlenie lineinymi sistemami pri vneshnikh vozmu-shcheniyakh: tekhnika lineinykh matrichnykh neravenstv (Control of Linear Systems under Exogenous Disturbances: The Technique of Linear Matrix Inequalities), Moscow: LENAND, 2014.

  15. Nazin, S.A., Polyak, B.T., and Topunov, M.V., Rejection of Bounded Exogenous Disturbances by the Method of Invariant Ellipsoids, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 467–486.

    Article  MathSciNet  MATH  Google Scholar 

  16. Leonessa, A., Haddad, W.M., and Hayakawa, T., Adaptive Tracking for Nonlinear Systems with Control Constraints, Proc. Amer. Control Conf., 2001, pp. 1292–1297.

  17. Lavretsky, E. and Hovakimyan, N., Positive μ-modification for Stable Adaptation in Dynamic Inversion Based Adaptive Control with Input Saturation, Proc. Amer. Control Conf., 2005, Portland, USA, pp. 3373–3378.

  18. Ioannou, P.A. and Sun, J., Robust Adaptive Control, PTR Prentice-Hall, 1996.

    MATH  Google Scholar 

  19. Narendra, K.S. and Annaswamy, A.M., Stable Adaptive Systems, Dover Publications, 2012.

    MATH  Google Scholar 

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Funding

This work was supported by the Russian Science Foundation (project no. 18-79-10104, https://rscf.ru/project/18-79-10104/).

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    I. B. Furtat, P. A. Gushchin & B. H. Nguyen

Authors
  1. I. B. Furtat
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  2. P. A. Gushchin
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  3. B. H. Nguyen
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Corresponding authors

Correspondence to I. B. Furtat, P. A. Gushchin or B. H. Nguyen.

Additional information

This paper was recommended for publication by by A.E. Polyakov, a member of the Editorial Board

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Furtat, I.B., Gushchin, P.A. & Nguyen, B.H. Control of Dynamic Systems under Input and Output Constraints. Autom Remote Control 84, 355–368 (2023). https://doi.org/10.1134/S0005117923040069

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  • DOI: https://doi.org/10.1134/S0005117923040069

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