Institute of Control Sciences, Russian Academy of Sciences (RAS)
Laboratory 7
ADAPTIVE AND ROBUST CONTROL SYSTEMS

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Last modified October 10, 2007.

Recent selected publications

Books:
  1. Boris T. Polyak, Pavel S. Shcherbakov. Robust stability and control. Moscow: Nauka, 2002. – 303 pages. (in Russian)
  2. Oleg N. Granichin, Boris T. Polyak. Randomised algorithms for estimation and optimization under almost arbitrary disturbances. Moscow: Nauka, 2003. – 291 pages. (in Russian)
 Polyak-Shcherbakov Granichin-Polyak

Journal papers and chapters in books:
  1. Polyak B.T. Convexity of quadratic transformations and its use in control and optimization. Journ. of Optimiz. Theory and Appl., 1998, vol. 99, No. 3, pp. 553-583. (pdf)
  2. Polyak B.T., Shcherbakov P.S. Random spherical uncertaintly in estimation and robustness. IEEE Trans. Autom. Control, 2000, vol. 45, No. 11, pp. 2145-2150. (pdf)
  3. Polyak B.T., Halpern M.  Optimal design for discrete-time linear systems via new performance index. Intern. Journ. Adaptive Contr. and Signal Proc., 2001, vol. 15, No.2, pp.129-152.
  4. Juditsky A.B., Nazin A.V.  On minimax approach to nonparametric adaptive control. Intern. Journ. Adaptive Contr. and Signal Proc., 2001, vol. 15, No.2, pp.153-168. (pdf)
  5. Polyak B.T.  Local programming. Comput. Mathematics and Math. Physics, 2001, vol. 41, No. 9, pp. 1324-1331. (pdf) (in Russian)
  6. Polyak B.T. Convexity of nonlinear image of a small ball with applications to optimization. Set-Valued Analysis, 2001, vol. 9, No. 1/2, pp. 159-168. (pdf)
  7. Calafiore G., Polyak B.T.  Stochastic algorithms for exact and approximate feasibility of robust LMIs. IEEE Trans. Autom. Contr., 2001, vol. 46, No. 11, pp. 1755-1759. (pdf)
  8. Polyak B.T., Tempo R.  Probabilistic robust design with linear quadratic regulators. Systems and Control Letters, 2001, vol. 43, No. 5, pp. 343-353. (pdf)
  9. Durieu C., Walter E., Polyak B.T.  Multi-input multi-output ellipsoidal state bounding. Journ. of Optimiz. Theory and Appl., 2001, vol. 111, No. 2, pp. 273-303. (pdf)
  10. Barmish B.R., Shcherbakov P.S.  On avoiding vertexization of robustness problems: the approximate feasibility concept. IEEE Trans. Autom. Contr., 2002, vol. 47, No.5, pp. 819-824. (pdf)
  11. Polyak B.T., Shcherbakov P.S.  Superstable linear control systems. 1. Analysis. Automation and Remote Control, 2002, vol. 63, No. 8, pp. 1239-1254. (pdf)
  12. Polyak B.T., Shcherbakov P.S.  Superstable linear control systems. 2. Design. Automation and Remote Control, 2002, vol. 63, No. 11, pp. 1745-1763. (pdf)
  13. Nazin A.V., Ljung L.  Asymptotically optimal smoothing of averaged LMS estimates for regression parameter tracking. Automatiña, 2002, vol. 38, No. 8, pp. 1287-1293. (pdf)
  14. Halpern M., Polyak B.T.  Optimization-based design of fixed-order controllers for command following. Automatica, 2002, vol. 38, No. 9, pp. 1615-1619. (pdf)
  15. Polyak B.T.  Robust linear algebra and robust aperiodicity. In: "Directions in Mathematical Systems Theory and Optimization" (A.Rantzer, C.I.Byrnes Eds.), Springer, 2003, pp. 249-260. (pdf)
  16. Dabbene F., Gay P., Polyak B.T.  Recursive algorithms for inner ellipsoidal approximation of convex polytopes. Automatica, 2003, vol. 39, No. 10, pp. 1773-1781. (pdf)
  17. Bouchard G., Girard S., Iouditski A.B., Nazin A.V.  Nonparametric frontier estimation by linear programming. Automation and Remote Control, 2004, vol. 65, No. 1, pp. 58-64. (pdf)
  18. Polyak B.T. Extended superstability in control theory. Automation and Remote Control, 2004, vol. 65, No. 4, pp. 1-10. (pdf)
  19. Poznyak A., Nazin A.V., Murano D.  Observer matrix gain optimization for stochastic continuous time nonlinear systems. Systems & Control Letters, 2004, vol. 52, No. 5, pp. 377-385. (pdf)
  20. Alexandrov A.G.  Reference-model adaptive control under external disturbances. Automation and Remote Control, 2004, vol. 65, No. 5, pp. 755-767. (pdf)
  21. Polyak B.T., Nazin S.A., Durieu C., Walter E.  Ellipsoidal parameter or state estimation under model uncertainty. Automatica, 2004, vol. 40, No. 7, pp. 1171-1179. (pdf)
  22. Polyak B.T., Nazin S.A.  Interval solution for interval algebraic equations. Mathematics and Computers in Simulation, 2004, vol. 66, No. 2-3, pp. 207-217. (pdf)
  23. Nazin A.V., Nazin S.A., Polyak B.T.  On Convergence of external ellipsoidal approximations of the reachability domains of discrete dynamic linear systems. Automation and Remote Control, 2004, vol. 65, No. 8, pp. 1210-1230. (pdf)
  24. Nazin S.A., Polyak B.T.  Interval parameter estimation under model uncertainty. Mathematical and Computer Modelling of Dynamical Systems, 2005, vol. 11, No. 2, pp. 225-237. (pdf)
  25. Bouchard G., Girard S., Iouditski A., Nazin A.V.  Some linear programming methods for frontier estimation. Applied Stochastic Models in Business and Industry, 2005, vol. 21, No. 2, pp.175-185. (pdf)
  26. Polyak B.T., Shcherbakov P.S.  Hard problems in linear control theory: possible approaches to solution. Automation and Remote Control, 2005, vol. 66, No. 5, pp. 681-718. (pdf)
  27. Alexandrov A.G., Orlov Yu.F.  Comparison of two methods of identification under unknown-but-bounded disturbances. Automation and Remote Control, 2005, vol. 66, No. 10, pp. 1647-1665. (pdf)
  28. Polyak B.T.  Stabilizing chaos with predictive control. Automation and Remote Control, 2005, vol. 66, No. 11, pp. 1791-1804. (pdf)
  29. Roll J., Nazin A., Ljung L.  Non-linear system identification via direct weight optimization. Automatica, Special Issue on “Data-Based Modelling and System Identification”, 2005, vol. 41, No. 3, pp. 475-490. (pdf)
  30. Girard S., Iouditski A., Nazin A.V.  L1-optimal nonparametric frontier estimation via linear programming. Automation and Remote Control, 2005, vol. 66, No. 12, pp. 2000-2018. (pdf)
  31. Iouditski A.B., Nazin A.V., Tsybakob A.B., Vayatis N.  Recursive aggregation of estimators by the mirror descent algorithm with averaging. Problems of Information Transmission, vol. 41, No. 4, 2005, pp. 368–384. (pdf)
  32. Gryazina E.N., Polyak B.T.  Stability regions in the parameter space: D-decomposition revisited. Automatica, 2006, vol. 42, No. 1, pp. 13-26. (pdf)
  33. Nesterov Yu.E., Polyak B.T.  Cubic regularization of Newton method and its global performance. Mathematical Programming, Ser. A, 2006, vol. 108, No. 1, pp. 177-205. (pdf)
  34. Polyak B.T.  Newton-Kantorovich method and its global convergence. Journal of Mathematical Sciences, 2006, vol. 133, No. 4, pp. 1513-1523. (pdf)
  35. Topunov M.V.  A class of µ-commutative bilinear control systems. Automation and Remote Control, 2006, vol. 67, No. 6, pp. 933-944. (pdf)
  36. Alexandrov A.G., Orlov Yu.F.  A frequency adaptive control for multidimensional systems. Automation and Remote Control, 2006, vol. 67, No. 7, pp. 1108–1122. (pdf)
  37. Polyak B.T.  New challenges in nonlinear control: stabilization and synchronization of chaos. In: “Forever Ljung in System Identification” (T.Glad and G.Hendeby Eds). Lund: Studentlitteratur, 2006, pp. 147-168. (pdf)
  38. Polyak B.T., Shcherbakov P.S.  The D-decomposition technique for linear matrix inequalities. Automation and Remote Control, 2006, vol. 67, No. 11, pp. 1847–1861. (pdf)
  39. Tremba A.A.  Robust D-decomposition under lp-bounded parametric uncertainties. Automation and Remote Control, 2006, vol. 67, No. 12, pp. 1878–1892. (pdf)
  40. Gryazina E.N., Polyak B.T., Tremba A.A. Design of the low-order controllers by the H¥ criterion: a parametric approach. Automation and Remote Control, 2007, vol. 68, No. 3, pp. 456–466. (pdf)
  41. Nazin S.A., Polyak B.T., Topunov M.V. Rejection of bounded exogenous disturbances by the method of invariant ellipsoids. Automation and Remote Control, 2007, vol. 68, No. 3, pp. 467–486. (pdf)
  42. Topunov M.V. On the existence of a smooth solution of a multidimensional boundary value problem. Differential Equations, 2007, vol. 43, No. 3, pp. 346–356. (pdf)
  43. Gryazina E.N. The geometry and number of the root invariant regions for linear systems. European Journal of Operational Research, 2007, vol. 181, No. 3, pp. 1166-1173. (pdf)
  44. Nazin S.A., Polyak B.T. Ellipsoid-based parameter estimation in the linear multidimensional systems with uncertain model description. Automation and Remote Control, 2007, vol. 68, No. 6, pp. 993–1005. (pdf)
  45. Dabbene F., Polyak B.T., Tempo R. On the complete instability of interval polynomials. Systems and Control Letters, 2007, vol. 56, No. 6, pp. 431-438. (pdf)

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