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Method of state space expansion in the design of autonomous control

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Abstract

The results of constructive analysis and block design of the problems of autonomous control in the nonlinear dynamic systems were presented. As compared with the well-known results of the control theory, the method of state space expansion enabled augmentation of the class of systems that are controlled autonomously in the output variables. The state observers on sliding modes were used for the dataware of the basic algorithms. The procedures developed feature multilevel decomposition of the problem of high-dimensionality design into smaller independent subproblems.

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References

  1. Morse, A.S. and Wonham, W.M., Status of Non-interacting Control, IEEE Trans. Automat. Control, 1971, vol. AC-16, no. 6, pp. 568–581.

    Article  MathSciNet  Google Scholar 

  2. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer, 1979. Translated under the title Linei’nye mnogomernye sistemy upravleniya: geometricheskii podkhod, Moscow: Nauka, 1980.

    MATH  Google Scholar 

  3. Utkin, V.A., Invariancy and Autonomy in Systems with Divisible Motions, Avtom. Telemekh., 2001, no. 11, pp. 73–94.

  4. Slotine, J.E. and Sastry, S.S., Tracking Control of Nonlinear Systems Using Sliding Surfaces with Application to Robot Manipulators, Int. J. Control, 1983, vol. 38, no. 2, pp. 465–492.

    Article  MATH  MathSciNet  Google Scholar 

  5. Utkin, V.A., Autonomy in the Multiple-input Multiple-output Systems with Discontinuous Controls, Avtom. Telemekh., 1983, no. 10, pp. 93–100.

  6. Krasnova, S.A. and Utkin, V.A., Kaskadnyi sintez nablyudatelei sostoyaniya nelineinykh mnogomernykh sistem (Cascaded Design of the State Observers of the Nonlinear Multiple-input Multiple-output Systems), Moscow: Nauka, 2006.

    Google Scholar 

  7. Freeman, R.A. and Kokotovic, P.V., Backstepping Design of Robust Controllers for Class of Nonlinear Systems, in Prepr. 2 IFAC Nonlinear Contr. Syst. Design Sympos., 1992, France, pp. 307–312.

  8. Utkin, V.A. and Krasnova, S.A., Blochnyi podkhod k sintezu zadachi slezheniya po vykhodnym peremennym (Block Approach to the Design of the Problem of Tracking by the Output Variables), Moscow: Inst. Probl. Upravlen., 2002, vol. XVII, pp. 102–110.

    Google Scholar 

  9. Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.

    Google Scholar 

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Original Russian Text © A.V. Utkin, 2007, published in Avtomatika i Telemekhanika, 2007, No. 6, pp. 81–98.

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Utkin, A.V. Method of state space expansion in the design of autonomous control. Autom Remote Control 68, 1006–1022 (2007). https://doi.org/10.1134/S0005117907060082

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  • DOI: https://doi.org/10.1134/S0005117907060082

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