ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 67 / January, 2024

DOI 10.17586/0021-3454-2017-60-5-398-403

UDC 681.51


S. V. Bystrov
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor

V. V. Grigoriev
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor

O. K. Mansurova
University of Mines, Department of Technological Process Automation and Production; Associate Professor

I. M. Pershin
North Caucasus Federal University, Pyatigorsk Institute; Department of Control in Technical and Biomedical Systems; Professor, Head of the Department

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Abstract. For continuous linear dynamic objects with a single inlet and outlet, a procedure of synthesis of polynomial (linear-quadratic) control laws is developed. The use of these control laws can improve the speed of convergence processes for large deviations while maintaining quality indicators processes for small deviations. Synthesis of control laws is based on the use of methods of optimal control theory by solving the Riccati type equation. The control laws are proved not to violate the asymptotic or exponential stability property depending on the type of stability adopted in design.
Keywords: linear quadratic control laws, optimality criteria, exponential stability, Riccati and Lyapunov matrix equations

  1. Krasovskiy A.A., Bukov V.N., Shendrik V.S. Universal'nye algoritmy optimal'nogo upravleniya nepreryvnymi protsessami (Universal Algorithms of Optimal Control of Continuous Processes), Moscow, 1977, 271 р. (in Russ.)
  2. Nair G.N., Evans R.I. Automatica, 2003, no. 39, рр. 585–593.
  3. Bryson A.E, Jr. & Ho Y.C. Applied optimal control: optimization, estimation, and control, Waltham, MA, Blaisdell, 1969, 481 p. 
  4. Furasov V.D. Ustoychivost' dvizheniya, otsenki i stabilizatsiya (The Stability of Motion, Estimates and Stabilization), Moscow, 1977, 247 р. (in Russ.)
  5. Voronov A.A. Osnovy teorii avtomaticheskogo upravleniya. Osobye lineynye i nelineynye sistemy (Fundamentals of the Theory of Automatic Control. Special Linear and Nonlinear Systems), Moscow, 1981, 303 р. (in Russ.)
  6. Grigoriev V.V., Mansurova. O.K. Qualitative exponential stability and instability of dynamical systems, Preprints of 5th IFAK Symp. on Nonlinear Control Systems (NOLCOS’01), St. Petersburg, 2001.
  7. Bystrov S.V., Grigoriev V.V. Universal Journal of Control and Automation, 2013, no. 1(1), рр. 15–18. DOI 10.13189.
  8. Bystrov S.V., Grigor'v V.V., Rabysh E.Yu., Mansurova O.K. Mehatronika, Avtomatizacia, Upravlenie (Mechatronics, Automation, Control), 2012, no. 9, рр. 32–36. (in Russ.)
  9.  Grigor'ev V.V., Bystrov S.V., Naumova A.K., Rabysh E.Yu., Cherevko N.A. Journal of Instrument Engineering, 2011, no. 6(54), рр. 24–30. (in Russ.)
  10. Bobtsov A.A., Bystrov S.V., Grigor'ev V.V., Dudrov P.V., Kozis D.V., Kostina O.V., Mansurova O.K. Mehatronika, Avtomatizacia, Upravlenie (Mechatronics, Automation, Control), 2006, no. 10, рр. 2–5. (in Russ.)
  11. Bystrov S.V., Grigor'ev V.V., Mansurova O.K., Pershin I.M. Mehatronika, Avtomatizacia, Upravlenie (Mechatronics, Automation, Control), 2013, no. 9, рр. 2–5. (in Russ.)
  12. Grigor'ev V.V., Motyl'kova M.M., Mansurova O.K. Journal of Instrument Engineering, 2007, no. 11(50), рр. 24–29. (in Russ.)