Skip to main content
SpringerLink
Log in

Review of Works by V. A. Yakubovich’s Scientific School on Artificial Intelligence and Robotics

  • TO THE 300th ANNIVERSARY OF SPbU
  • Published:
Vestnik St. Petersburg University, Mathematics Aims and scope Submit manuscript

Abstract

This is a review of the works of the research school of V.A. Yakubovich in the field of artificial intelligence, machine learning, adaptive systems, and robotics. The method of recurrent objective inequalities is considered in detail. The significance of the presented results for the further development of cybernetics and artificial intelligence is discussed. Special emphasis is put on Yakubovich’s seminal works on machine learning and development of the concept of finitely convergent algorithms for solving recurrent objective inequalities. Typical results of their convergence are discussed in detail as a specific illustration. The study distinguishes the contribution of the school to the formation and development of modern theories of adaptive control and mathematical robotics, particularly, the theory of adaptive robots. A special section is devoted to adaptive suboptimal control.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Notes

  1. Naturally, the numbering of the theorems exposed below does not consider Theorem 1 from Yakubovich’s article [7] in Fig. 4.

REFERENCES

  1. A. L. Fradkov, “V. A. Yakubovich’s scientific school of theoretical cybernetics at the St. Petersburg (Leningrad) University,” in The History of Computer Science and Cybernetics in St. Petersburg (Leningrad), Ed. by R. M. Yusu-pov (Nauka, St. Petersburg, 2008), Vol. 1, pp. 79–83 [in Russian].

    Google Scholar 

  2. A. L. Fradkov and A. I. Shepeljavyi, “The history of cybernetics and artificial intelligence. a view from Saint Petersburg,” Cybern. Phys. 11, 253–263 (2022).

    Article  Google Scholar 

  3. S. V. Gusev and V. A. Bondarko, “Notes on Yakubovich’s method of recursive objective inequalities and its application in adaptive control and robotics,” in Proc. IFAC World Congr. 2020, Berlin, Germany, July 12–17, 2020 (International Federation of Automatic Control, New York, 2020).

  4. A. L. Fradkov, “Early history of machine learning,” in Proc. IFAC World Congr. 2020, Berlin, Germany, July 12–17, 2020 (International Federation of Automatic Control, New York, 2020).

  5. A. M. Annaswamy and A. L. Fradkov, “Historical perspective of adaptive control and learning,” Annu. Rev. Control 52, 18–41 (2021). https://doi.org/10.48550/arXiv.2108.11336

    Article  MathSciNet  Google Scholar 

  6. A. L. Fradkov and B. T. Polyak, “Adaptive and robust control in the USSR,” IFAC-PapersOnLine 53 (2), 1373–1378 (2020). https://doi.org/10.1016/j.ifacol.2020.12.1882

    Article  Google Scholar 

  7. V. A. Yakubovich, “Machines learning pattern recognition.” in Methods of Computation (Leningr. Gos. Univ., Leningrad, 1963), Vol. 2, pp. 95–131 [in Russian].

    Google Scholar 

  8. V. A. Yakubovich, “Machines learning pattern recognition,” Vestn. St. Petersburg Univ.: Math. 54, 384–394 (2021); Vestn. St. Petersburg Univ.: Math. 55, 71–86 (2022). https://doi.org/10.1134/S106345412201015010.1134/S1063454122010150https://doi.org/10.1134/S106345412104021X

  9. V. A. Yakubovich, “Some general theoretical principles of the construction of trainable identification systems. I.” in Computing Machines and Problems of Programming (Leningr. Gos. Univ., Leningrad, 1965), pp. 3–71 [in Russian].

    Google Scholar 

  10. V. A. Yakubovich, “Finitely-convergent recurrent algorithms for solving objective inequalities,” Dokl. Akad. Nauk SSSR 166, 1308–1312 (1966).

    MathSciNet  Google Scholar 

  11. V. A. Yakubovich, “Theory of adaptive systems,” Sov. Phys. Dokl. 13, 852–856 (1968).

    MathSciNet  Google Scholar 

  12. V. A. Yakubovich, “Adaptive systems with multistep goal conditions,” Dokl. Akad. Nauk SSSR 183, 303–306 (1968).

    MathSciNet  Google Scholar 

  13. A. Kh. Gelig and V. A. Yakubovich, “Application of a trainable recognition system to isolate a signal from noise,” in Computing Machines and Problems of Cybernetics (Leningr. Gos. Univ., Leningrad, 1968), Vol. 5, pp. 95–100 [in Russian].

    Google Scholar 

  14. V. A. Yakubovich, “On certain problem of self-learning expedient behaviour,” Autom. Remote Control 30, 1292–1310 (1969).

    Google Scholar 

  15. V. A. Yakubovich, “On organization of the "brain” of a certain class of systems that develop appropriate behavior (solved and unsolved problems),” in Proc. 4th All-Union Conf. on Neurocybernetics, Rostov, 1970 (Rostov. Gos. Univ., 1970), p. 152.

  16. G. D. Penev and V. A. Yakubovich, “On some tasks of adaptive behavior,” Dokl. Akad. Nauk SSSR 198, 787–790 (1971).

    Google Scholar 

  17. V. A. Yakubovich and A. V. Timofeev, “On a class of self-learning systems possessing appropriate behavior,” in Control and Informational Process in Nature (Nauka, Moscow, 1971), pp. 111–113 [in Russian].

    Google Scholar 

  18. A. V. Timofeev, V. V. Kharichev, A. A. Shmidt, and V. A. Yakubovich, “One task of image recognition and description,” in Biological, Medical Cybernetics and Bionics (Nauchn. Sov. Kibern. i Inst. Kibern., Kiev, 1971) [in Russian].

  19. S. V. Gusev, A. V. Timofeev, and V. A. Yakubovich, “Adaptation in robotic systems with artificial intelligence,” in Proc. 7th All-Union Meeting on Control Problems, Minsk, 1977, pp. 279–282.

  20. V. N. Vapnik, “Machines learning pattern recognition,” in Pattern Recognition Learning Algorithms (Sov. Radio, Moscow, 1973), pp. 5–24 [in Russian].

    Google Scholar 

  21. B. N. Kozinets, R. M. Lantsman, and V. A. Yakubovich, “Forensic examination of close handwriting using electronic computers,” Dokl. Akad. Nauk SSSR 167, 1008–1011 (1966).

    Google Scholar 

  22. B. N. Kozinets, “About a linear perceptron learning algorithm,” in Computing Machines and Problems of Programming (Leningr. Gos. Univ., Leningrad, 1964), Vol. 3, pp. 80–83.

    Google Scholar 

  23. B. F. Mitchell, V. F. Dem’yanov, and V. N. Malozemov, “Finding the point closest to the origin of the polyhedron,” Vestn. Leningr. Gos. Univ., Ser. 1: Mat., Mekh., Astron., No. 19, 38–45 (1971).

  24. B. F. Mitchel, V. V. Dem’yanov, and V. N. Malozemov, “Finding the point of a polyhedron closest to the origin,” SIAM J. Control 12, 19–26 (1974).

    Article  MathSciNet  Google Scholar 

  25. V. N. Malozemov, “On the fortieth anniversary of MDM-method,” Vestn. Syktyvkarskogo Univ., No. 15, 51–62 (2012).

  26. V. N. Vapnik and A. Ya. Chervonenkis, “On a certain class of perceptrons,” Avtom. Telemekh. 25, 112–120 (1964).

    Google Scholar 

  27. V. A. Yakubovich, “ Finitely convergent algorithms for the solution of countable systems of inequalities, and their application in problems of the synthesis of adaptive systems,” Sov. Phys. Dokl. 14, 1051–1054 (1970).

    MathSciNet  Google Scholar 

  28. V. N. Fomin, “Stochastic analogs of finitely convergent learning algorithms for recognition systems,” in Computing Machines and Problems of Programming (Leningr. Gos. Univ., Leningrad, 1971), Vol. 6, pp. 68–87 [in Russian].

    Google Scholar 

  29. A. L. Fradkov, “Some finitely converging solution algorithms for infinite systems of inequalities and their application in the theory of adaptive systems,” Vest. Leningr. Gos. Univ., Ser. 1: Mat., Mekh. Astron., No. 19, 70–75 (1972).

  30. V. N. Fomin, Mathematical Theory of Trainable Recognition Systems (Leningr. Gos. Univ., Leningrad, 1976) [in Russian].

    Google Scholar 

  31. D. P. Derevitskii and A. L. Fradkov, Applied Theory of Discrete Adaptive Control Systems (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  32. V. A. Bondarko and V. A. Yakubovich, “The method of recursive aim inequalities in adaptive control theory,” Int. J. Adaptive Control Signal Process. 6, 141–160 (1992).

    Article  Google Scholar 

  33. A. L. Fradkov, Adaptive Control of Complex Systems (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  34. S. V. Gusev, “A finite convergent algorithm for restoring the regression function and its use in adaptive control problems,” Autom. Remote Control 50, 367–374 (1989).

    Google Scholar 

  35. V. A. Bondarko, “Adaptive suboptimal systems with a variable dimension of the vector of adjustable parameters,” Autom. Remote Control 67, 1732–1751 (2006).

    Article  MathSciNet  Google Scholar 

  36. S. V. Gusev, A. V. Timofeev, and V. A. Yakubovich, “On a hierarchical system of integral robot control,” in Proc. 6th Joint Conf. on Artificial Intelligence, Moscow, 1975 (Inst. Probl. Upr. Akad. Nauk SSSR, Moscow, 1975), pp. 76–85.

  37. G. G. Grigor’ev, S. V. Gusev, V. V. Nesterov, and V. A. Yakubovich, “Mobile robot-manipulator adaptive control,” in Adaptive Robots-82: Proc. All-Union Sci. and Tech. Conf., Nalchik, Sept. 14–16, 1982 (TsNPTO Priborostr. Prom-sti., Nalchik, 1982), pp. 89–91.

  38. A. V. Timofeev, Robots and Artificial Intelligence (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  39. V. N. Fomin, A. L. Fradkov, and V. A. Yakubovich, Adaptive Control of Dynamic Systems (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  40. A. Kh. Gelig, Dynamics of Impulse Systems and Neural Networks (Leningr. Gos. Univ., Leningrad, 1982) [in Russian].

    Google Scholar 

  41. R. M. Granovskaya and I. Ya. Bereznaya, Intuition and Artificial Intelligence (Leningr. Gos. Univ., Leningrad, 1991) [in Russian].

    Google Scholar 

  42. A. V. Savkin, T. M. Cheng, Z. Xi, F. Javed, A. S. Matveev, and H. Nguyen, Decentralized Coverage Control Problems for Mobile Robotic Sensor and Actuator Networks (IEEE/Wiley, New York, 2015).

    Book  Google Scholar 

  43. A. S. Matveev, A. V. Savkin, M. C. Hoy, and C. Wang, Safe Robot Navigation among Moving and Steady Obstacles (Elsevier/Butterworth Heinemann, Oxford, UK, 2016).

    Google Scholar 

  44. M. Hoy, A. S. Matveev, and A. V. Savkin, “Algorithms for collision-free navigation of mobile robots in complex cluttered environments: A survey,” Robotica 33, 463–497 (2015).

    Article  Google Scholar 

  45. V. A. Yakubovich, “Adaptive suboptimal control of a linear dynamic object in the presence of a delay in control,” Kibernetika 1, 26–43 (1976).

    Google Scholar 

  46. V. A. Bondarko and V. A. Yakubovich, “Synthesis of a suboptimal adaptive system with a reference model for controlling a discrete linear dynamic object,” in Adaptation and Training in Control and Decision-Making Systems (Nauka, Novosibirsk, 1982), pp. 10–27 [in Russian].

    Google Scholar 

  47. F. Lewis and D. Vrabie, “Reinforcement learning and adaptive dynamic programming for feedback control,” IEEE Circ. Syst. Mag. 9, 32–50 (2009).

    Article  Google Scholar 

  48. F. Lewis, D. Vrabie, and K. G. Vamvoudakis, “Reinforcement learning and feedback control: Using natural decision methods to design optimal adaptive controllers,” IEEE Circ. Syst. Mag. 32, 30 (2012).

    MathSciNet  Google Scholar 

  49. R. S. Sutton, A. G. Barto, and R. J. Williams, “Reinforcement learning is direct adaptive optimal control,” IEEE Control Syst. Mag. 12, 19–22 (1992).

    Article  Google Scholar 

  50. X. Yang, D. Liu, and D. Wang, “Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints,” Int. J. Control 87, 553– 566 (2014).

    Article  MathSciNet  Google Scholar 

  51. B. Recht, “A tour of reinforcement learning: The view from continuous control,” Annu. Rev. Control Robot. Auton. Syst. 2, 253–279 (2019).

    Article  Google Scholar 

  52. B. T. Bian and Z.-P. Jiang, “Value iteration, adaptive dynamic programming, and optimal control of nonlinear systems,” in Proc. IEEE 55th Conf. on Decision and Control, Las Vegas, Nev., Dec. 12–14, 2016 (IEEE, Piscataway, N.J., 2016).

  53. M. Lipkovich, “Yakubovich’s method of recursive objective inequalities in machine learning,” IFAC-PapersOnLine 55 (12), 138–143 (2022).

    Article  Google Scholar 

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    A. S. Matveev, A. L. Fradkov & A. I. Shepeljavyi

Authors
  1. A. S. Matveev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Fradkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. I. Shepeljavyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. S. Matveev, A. L. Fradkov or A. I. Shepeljavyi.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by S. Kuznetsov

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matveev, A.S., Fradkov, A.L. & Shepeljavyi, A.I. Review of Works by V. A. Yakubovich’s Scientific School on Artificial Intelligence and Robotics. Vestnik St.Petersb. Univ.Math. 56, 478–492 (2023). https://doi.org/10.1134/S106345412304009X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106345412304009X

Keywords:

Search

Navigation