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Theory of nonlinear feedback under uncertainty

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References

1. Books

  1. S. V. Emel'yanov, Binary Automatic Control Systems [in English] Mir, Moscow (1987).

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  2. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, Global Controllability and Stabilization of Nonlinear Systems [in Russian], unpublished manuscript, VINITI 17.01.91, N286-V91 (1991).

2. Monographs

  1. S. V. Emel'yanov, Binary Automatic Control Systems [in Russian], Series “Binary Dynamic Systems,” No. 1, MNIIPU, Moscow (1984).

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  2. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, Binary Control Systems for Nonstationary Processes Using Adaptive and Multiplicative Feedback [in Russian], Series “Binary Dynamic Systems,” No. 2, MNIIPU, Moscow (1983).

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  3. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, Binary Control Systems for Free Motion of Dynamic Systems [in Russian], Series “Binary Dynamic Systems,” No. 3, MNIIPU, Moscow (1983).

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  4. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, Binary Control Systems for Forced Motion of Dynamic Systems [in Russian], Series “Binary Dynamic Systems,” No. 4, MNIIPU, Moscow (1984).

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  5. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, Quasicontinuous controls in nonstationary binary dynamic systems [in Russian], Series “Binary Dynamic Systems,” No. 5, MNIIPU, Moscow (1984).

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3. Surveys

  1. S. V. Emel'yanov and S. K. Korovin, “New types of feedback and their use in closed-loop dynamic systems,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 15, 145–216, VINITI, Moscow (1982).

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  2. S. V. Emel'yanov and S. K. Korovin, “Application of new types of feedback in control problems for nonstationary dynamic systems,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 16, 70–155, VINITI, Moscow (1983).

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  3. S. V. Emel'yanov and S. K. Korovin, “Discrete binary control systems,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 17, 73–167, VINITI, Moscow (1984).

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  4. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Vector control of nonlinear systems in the class of binary control systems,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 18, 3–44, VINITI, Moscow (1985).

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  5. S. V. Emel'yanov and M. M. Denisov, “Methods of signal separation using the spectrum of a discrete parameter,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 19, 3–68, VINITI, Moscow (1986).

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  6. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Controllability of nonlinear systems. Two-Dimensional Systems,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 21, 3–67, VINITI, Moscow (1987).

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  7. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Nonlinear systems. Controllability, stabilizability, invariance,” Itogi Nauki i Tekhniki. Tekhnicheskaya Kibernetika, Vol. 23, 3–107, VINITI, Moscow (1988).

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4. Articles published in Doklady Akademii Nauk SSSR

  1. S. V. Emel'yanov and S. K. Korovin, “Application of the principle of control by deviation to extend the set of feedback types,”258, No. 5, 1070–1074 (1981).

  2. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Synthesis of nonlinear control for free motion of nonstationary systems,”265, No. 2, 297–301 (1982).

  3. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Synthesis of control systems using coordinate-parametric and parametric feedback,”266, No. 5, 1077–1081 (1982).

  4. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Synthesis of control systems with quasicontinuous generation of controls,”268, 1067–1071 (1983).

  5. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Design principles and general synthesis methods of binary control systems for uncertain nonlinear systems,”281, No. 4, 810–814 (1985).

  6. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Synthesis of vector control for uncertain nonlinear systems,”283, No. 5, 1111–1116 (1985).

  7. S. V. Emel'yanov, S. K. Korovin, and I. G. Mamedov, “Quasi-decoupling method and its application for control system synthesis,”286, No. 2, 311–315 (1986).

  8. S. V. Emel'yanov, S. K. Korovin, and L. V. Levantovskii, “High-order sliding modes in binary control systems,”287, No. 6, 1338–1342 (1986).

  9. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and S. V. Nikitin, “Controllability criteria of nonlinear systems with phase constraints,”290, No. 1, 18–22 (1986).

  10. S. V. Emel'yanov, S. V. Nikitin, and V. I. Sizikov, “Optimization approach to control of systems with uncertain dynamics,”291, No. 5, 1075–1079 (1986).

  11. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Controllability criteria for two-dimensional nonlinear systems in a region with control constraints,”294, No. 6, 1310–1314 (1987).

  12. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Classification of singularities and controllability criterion of bilinear systems in a plane,”295, No. 1, 42–46 (1987).

  13. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Controllability of nonlinear systems and systems on a foliation,”299, No. 3, 573–576 (1988).

  14. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Controllability analysis by methods of the theory of approximative groups and systems on foliations,”300, No. 4, 821–823 (1988).

  15. S. V. Emel'yanov, S. K. Korovin, S. V. Nikitin, and M. G. Nikitina, “Observers and output differentiators in nonlinear systems,”306, No. 3, 556–560 (1989).

  16. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and A. P. Nosov, “Asymptotic invariance in control problems for uncertain systems,”311, No. 1, 44–49 (1990).

  17. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and A. P. Nosov, “Asymptotic invariance and robust stabilization of hereditary systems with continuous control,”311, No. 2, 296–300 (1990).

  18. S. V. Emel'yanov, S. K. Korovin, A. L. Nersisyan, and Yu. E. Nisenzon, “Output stabilization of uncertain systems by discontinuous control,”311, No. 3, 544–549 (1990).

  19. S. V. Emel'yanov, S. K. Korovin, and A. L. Nersisyan, “Asymptotic properties of state observers for uncertain systems with a distinguished stationary linear part,”311, No. 4, 807–811 (1990).

  20. S. V. Emel'yanov, S. K. Korovin, A. L. Nersisyan, and Yu. E. Nisenzon, “Output stabilization of multidimensional uncertain systems,”311, No. 5, 1062–1067 (1990).

  21. S. V. Emel'yanov, S. K. Korovin, and A. L. Nersisyan, “Stabilization of uncertain neutral systems by a variable structure controller,”312, No. 4, 801–806 (1990).

  22. S. V. Emel'yanov, P. V. Zhivoglyadov, S. K. Korovin, and S. V. Nikitin, “Semigroup approach to description of the class of admissible disturbances,”313, No. 5, 1057–1061 (1990).

  23. S. V. Emel'yanov, S. K. Korovin, A. L. Nersisyan, and Yu. E. Nisenzon, “Asymptotic observers for a class of nonlinear dynamic systems,”313, No. 5, 1052–1056 (1990).

  24. S. V. Emel'yanov, P. V. Zhivoglyadov, S. K. Korovin, and S. V. Nikitin, “Stability criteria for a convex polyhedron of entire functions,”315, No. 3, 551–553 (1990).

  25. S. V. Emel'yanov, S. K. Korovin, M. G. Nikitina, and S. V. Nikitin, “A finite-dimensional stabilizer for distributed parameter systems: Sakawa controller,”315, No. 4, 798–803 (1990).

  26. S. V. Emel'yanov, S. K. Korovin, M. G. Nikitina, and S. V. Nikitin, “Approximative controllability and observability of infinite-dimensional systems,”315, No. 4, 1052–1056 (1990).

  27. S. V. Emel'yanov, P. V. Zhivoglyadov, S. K. Korovin, and S. V. Nikitin, “Principle of recursive stability of disturbances in robust stabilization problem,”316, No. 4, 834–838 (1991).

  28. S. V. Emel'yanov, P. V. Zhivoglyadov, and S. K. Korovin, “A stabilization technique for discrete systems with compact uncertainty,”319, 91–97 (1991).

5. Papers published in journals of the Academy of Sciences of USSR and other publications in Russian

  1. S. V. Emel'yanov and S. K. Korovin, “Extension of the set of feedback types and their use for constructing closed-loop dynamic systems,” Tekhn. Kibern., No. 5, 173–183 (1981).

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  2. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Design principles and properties of control systems with integral coordinate-parametric feedback,” Tekhn. Kibern., No. 6, 140–152 (1981).

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  3. S. V. Emel'yanov, S. K. Korovin, and V. I. Sizikov, “Control of free motion of dynamic systems using coordinate-parametric and parametric feedback,” Tekhn. Kibern., No. 4, 136–142 (1982).

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  4. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Control of nonstationary dynamic systems using coordinate-parametric feedback,” Tekhn. Kibern., No. 6, 201–212 (1982).

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  5. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Control of nonstationary dynamic systems using coordinate-parametric and parametric feedback,” Tekhn. Kibern., No. 4, 158–167 (1983).

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  6. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Control of linear stationary systems in the presence of external disturbances using feedback of various types,” Tekhn. Kibern., No. 1, 174–182 (1984).

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  7. S. V. Emel'yanov, V. B. Gavrilov, and A. A. Solov'ev, “Discrete differentiation algorithm based on a binary structure,” Tekhn. Kibern., No. 6, 93–101 (1985).

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  8. S. V. Emel'yanov, S. K. Korovin, and L. V. Levantovskii, “Second order sliding modes in control of uncertain systems,” Tekhn. Kibern., No. 1, 112–118 (1986).

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  9. S. V. Emel'yanov, S. K. Korovin, and I. G. Mamedov, “Structural transformations and spatial decomposition of discrete controlled systems: quasi-decoupling method,” Tekhn. Kibern., No. 6, 118–128 (1986).

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  10. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and S. V. Nikitin, “Controllability criteria of nonlinear dynamic systems in a plane with phase constraints,” Tekhn. Kibern., No. 6, 108–114 (1987).

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  11. S. K. Korovin, I. G. Mamedov, and A. P. Mamedova, “Stability uniform in a small parameter and stabilization of discrete singularly perturbed dynamic systems,” Tekhn. Kibern., No. 1, 21–29 (1989).

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  12. S. K. Korovin, A. L. Nersisyan, and Yu. E. Nisenzon, “Output control of linear uncertain systems,” Tekhn. Kibern., No. 1, 67–73 (1990).

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  13. S. V. Emel'yanov and A. A. Solov'ev, “Analysis of the behavior of solutions of a nonhomogeneous system of differential equations with a discontinuous right-hand side,” Diff. Uravn., Minsk,22, 768–774 (1986).

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  14. S. V. Emel'yanov, S. K. Korovin, and B. V. Ulanov, “Control of nonstationary dynamic systems,” Diff. Uravn.,20, No. 10, 1683–1691 (1984).

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  15. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and A. L. Nersisyan, “Binary control algorithms for a class of delayed uncertain dynamic systems,” Diff. Uravn.,25, No. 10, 1670–1679 (1989).

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  16. S. V. Emel'yanov, S. K. Korovin, I. G. Mamedov, and A. P. Nosov, “Asymptotic invariance of delayed control systems,” Diff. Uravn.,27, No. 3, 415–427 (1991).

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  17. S. K. Korovin, I. G. Mamedov, and A. P. Nosov, “Suboptimality of asymptotically invariant control systems,” Diff. Uravn.,28, No. 11, 1932–1945 (1992).

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  18. S. V. Emel'yanov, P. V. Zhivoglyadov, S. K. Korovin, and S. V. Nikitin, “Asymptotic behavior of admissible parametric disturbances in the stabilization problem for an uncertain discrete system,” Avtomat. Telemekh., No. 7, 41–52 (1991).

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  19. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Global controllability and stabilization of nonlinear systems,” Matem. Modelirovanie,1, No. 1, 51–90 (1989).

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  20. S. V. Emel'yanov, S. K. Korovin, and L. V. Levantovskii, “A new class of second-order sliding algorithms,” Matem. Modelirovanie,2, No. 3, 89–100 (1990).

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  21. S. V. Emel'yanov, “Closed-loop dynamic systems with feedback control,” Avtomat. i Izchisl. Tekhn., Sofia,14, No. 2, 5–20 (1983).

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  22. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Two-dimensional bilinear systems: classification of singularities and controllability,” Informatika, Upravlenie, Vychisl. Tekhn., No. 1, 59–83, Mashinostroenie (1987).

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  23. S. V. Emel'yanov, A. P. Nosov, and V. I. Sizikov, “Binary control of uncertain systems with memory,” Izv. Vuzov, ser. Priborostroenie,31, No. 2, 11–18 (1988).

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  24. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Nonlinear systems. Design of observers and output differentiators,” in: Theory of Complex Systems and Simulation Methods [in Russian], No. 1, VNIISI, Moscow (1988), pp. 4–13.

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  25. S. V. Emel'yanov, S. K. Korovin, S. V. Nikitin, and V. I. Sizikov, “Stabilization of two-dimensional systems,” in: Theory of Complex Systems and Simulation Methods [in Russian], No. 1, VNIISI, Moscow (1988), pp. 14–18.

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  26. S. V. Emel'yanov, S. K. Korovin, and S. V. Nikitin, “Application of the theory of foliations and approximative groups for controllability analysis of nonlinear systems,” in: Optimality of Controlled Dynamic Systems [in Russian], No. 19, VNIISI, Moscow (1988), pp. 4–12.

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  27. S. K. Korovin, A. L. Nersisyan, and Yu. E. Nisenzon, “Output stabilization of a class of uncertain systems,” in: Optimization of Controlled Systems [in Russian], No. 1, VNIISI, Moscow (1990), pp. 62–68.

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  28. P. V. Zhivoglyadov and S. K. Korovin, “Stabilization of uncertain discrete systems by localization method,” in: Control of Nonlinear Systems [in Russian], No. 4, VNIISI, Moscow (1991), pp. 75–98.

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  29. V. N. Akhtyrskii, S. K. Korovin, and V. I. Sizikov, “Binary control systems with inertial coordinate-operator feedback,” in: Mathematical Modeling [in Russian], Metallurg, Moscow (1990), pp. 5–22.

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6. Articles Published in English

  1. S. V. Emelyanov and S. K. Korovin, “Development of feedback types and their application to design of closed-loop dynamic systems,” Probl. Contr. Inform. Theory,10, No. 3, 161–174 (1981).

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  2. S. V. Emelyanov, S. K. Korovin, and V. I. Sizikov, “Use of coordinate-parametric feedback in design of control systems,” Probl. Contr. Inform. Theory,10, No. 4, 237–251 (1981).

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  3. S. V. Emelyanov, S. K. Korovin, and V. I. Sizikov, “Control of non-stationary plants with coordinate-parametric and parametric feedbacks,” Probl. Contr. Inform. Theory,11, No. 4, 259–269 (1982).

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  4. S. V. Emelyanov, S. K. Korovin, and B. V. Ulanov, “Control of nonstationary dynamic systems with quasicontinuous generation of the control signal,” Probl. Contr. Inform. Theory,12, No. 1, 11–32 (1983).

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  5. S. V. Emelyanov and A. A. Soloviev, “Application of new feedback types in the problem of signal differentiation,” Probl. Contr. Inform. Theory,12, No. 2, 63–77 (1983).

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  6. S. V. Emelyanov, S. K. Korovin, and B. V. Ulanov, “Control of dynamic systems in face of exogenous signals with feedbacks of various types,” Probl. Contr. Inform. Theory,14, No. 1, 3–16 (1985).

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  7. S. V. Emelyanov, S. K. Korovin, and L. V. Levantovskiy, “A drift algorithm in control of uncertain processes,” Probl. Contr. Inform. Theory,15, No. 6, 425–538 (1986).

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  8. S. V. Emelyanov, S. K. Korovin, and I. G. Mamedov, “Structural transformations and spatial decompositions of control systems: the quasi-decoupling method,” Probl. Contr. Inform. Theory,16, No. 3, 155–168 (1987).

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  9. S. V. Emelyanov, S. K. Korovin, I. G. Mamedov, and A. L. Nersisyan, “Stabilization of uncertain dynamic delayed processes by binary control systems,” Probl. Contr. Inform. Theory,18, No. 3, 135–149 (1989).

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  10. S. V. Emelyanov, S. K. Korovin, and S. V. Nikitin, “Global controllability and stabilization of nonlinear systems,” Probl. Contr. Inform. Theory,18, No. 3, 161–174 (1989).

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  11. S. V. Emelyanov, P. V. Zhivoglyadov, S. K. Korovin, and S. V. Nikitin, “Groups of isometries and some stabilization and stabilizability aspects of uncertain systems,” Probl. Contr. Inform. Theory,19, No. 5–6, 451–577 (1990).

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  12. S. V. Emelyanov, P. V. Zhivoglyadov, and S. K. Korovin, “Analysis of admissible perturbations and stabilization of uncertain discrete-time plants,” Probl. Contr. Inform. Theory,20, No. 5, 353–371 (1991).

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  13. S. V. Emelyanov, S. K. Korovin, and S. V. Nikitin, “Nonlinear Kronecker's characteristics and its application,” Preprints 11th IFAC World Congress, Tallinn, Estonia, Vol. 6, pp. 1–4 (Aug. 1990).

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  14. S. K. Korovin, M. G. Nikitina, and S. V. Nikitin, “Infinite-dimensional systems: Approximate controllability and observability, part 1,” Probl. Contr. Inform. Theory,20, No. 1, 59–76 (1991).

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  15. S. K. Korovin, M. G. Nikitina, and S. V. Nikitin, “Infinite-dimensional systems: Design of Sakawa controllers, part 2,” Probl. Contr. Inform. Theory,20, No. 2, 97–111 (1991).

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  16. S. V. Emelyanov, S. K. Korovin, A. L. Nersisian, and Y. Y. Nisenzon, “Discontinuous output stabilizing an uncertain MIMO plant,” Int. J. Contr.,55, No. 1, 83–107 (1992).

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Authors
  1. S. V. Emel'yanov
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  2. S. K. Korovin
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Additional information

M. V. Lomonosov Moscow State University. Translated from Matematicheskoe Modelirovanie. Published by Moscow University, Moscow, 1993, pp. 214–278.

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Emel'yanov, S.V., Korovin, S.K. Theory of nonlinear feedback under uncertainty. Comput Math Model 7, 38–87 (1996). https://doi.org/10.1007/BF01128748

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