TOChNYE APPROKSIMATsII MNOZhESTV S VEROYaTNOSTNYMI OGRANIChENIYaMI S POMOShch'Yu PAKETNOGO VEROYaTNOSTNOGO MASShTABIROVANIYa

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Рұқсат ақылы немесе тек жазылушылар үшін

Аннотация

Вычисление "надежных" в вероятностном смысле областей остается актуальной проблемой в стохастических постановках задач теории систем. В данной работе представлена основанная на случайной выборке процедура для получения "точных" внутренних аппроксимаций вероятностно-надежной области. Предлагаемый подход не требует каких-либо предположений о распределении вероятностей, а внутренняя аппроксимация может быть найдена в автономном режиме (офлайн).

Әдебиет тізімі

  1. Bemporad A., Morari, M. Robust model predictive control: A survey / Robustness in Identification and Control. Lecture Notes in Control and Information Sciences. Garulli A., Tesi A. (Eds.). London: Springer, 1999. V. 245.
  2. Mayne D., Seron M., Rakovic S. Robust model predictive control of constrained linear systems with bounded disturbances // Automatica. 2005. V. 41. No. 2. P. 219–224.
  3. Mayne D., Rakovic S., Findeisen R., Allgöwer F. Robust output feedback model predictive control of constrained linear systems // Automatica. 2006. V. 42. No. 7. P. 1217–1222.
  4. Lorenzen M., Dabbene F., Tempo R., Allgöwer F. Constraint-tightening and stability in stochastic model predictive control // IEEE Transactions on Automatic Control. 2016. V. 62. No. 7. P. 3165–3177.
  5. Farina M., Giulioni L., Scattolini R. Stochastic linear model predictive control with chance constraints – a review // J. Process Control. 2016. V. 44. P. 53–67.
  6. Mesbah A. Stochastic model predictive control: An overview and perspectives for future research // IEEE Control Systems Magazine. 2016. V. 36. No. 6. P. 30–44.
  7. Charnes A., Cooper W. Chance constraints and normal deviates // J. Amer. Stat. Associat. 1962. V. 57. No. 297. P. 134–148.
  8. Kücükyaouz S., Jiang, R. Chance-constrained optimization under limited distributional information: A review of reformulations based on sampling and distributional robustness // EURO J. Comput. Optim. 2022. V. 10. Art. No. 100030.
  9. Mammarella M., Mirasierra V., Lorenzen M., Alamo T., Dabbene F. Chance-constrained sets approximation: A probabilistic scaling approach // Automatica. 2022. V. 137. Art. No. 110108.
  10. Polyak B., Tempo R. Probabilistic robust design with linear quadratic regulators // Syst. Control Lett. 2001. V. 43. No. 5. P. 343–353.
  11. Calaftore G., Polyak B. Stochastic algorithms for exact and approximate feasibility of robust LMIs // IEEE Transactions on Automatic Control. 2001. V. 46. No. 11. P. 1755–1759.
  12. Dabbene F., Gay P., Polyak B. Recursive algorithms for inner ellipsoidal approximation of convex polytopes // Automatica. 2003. V. 39. P. 1773–1781.
  13. Calaftore G., Campi M. The scenario approach to robust control design // IEEE Transactions on Automatic Control. 2006. V. 51. No. 5. P. 742–753.
  14. Tempo R., Calafiore G., Dabbene F. Randomized Algorithms for Analysis and Control of Uncertain Systems, with Applications. London: Springer, 2013.
  15. Polyak B., Shcherbakov P. Randomization in robustness, estimation, and optimization // Uncertainty in Complex Networked Systems: In Honor of Roberto Tempo. Basar T. (Ed.). Cham: Springer, 2018. P. 181–208.
  16. Kataoka S. A stochastic programming model // Econometrica: J. Econom. Soc. 1963. P. 181–196.
  17. Prekopa A. Logarithmic concave measures with application to stochastic programming // Acta Scientiarum Mathematicarum. 1971. V. 32. P. 301–316.
  18. Geng X., Xie L. Data-driven decision making in power systems with probabilistic guarantees: Theory and applications of chance-constrained optimization // Ann. Rev. Control. 2019. V. 47. P. 341–363.
  19. Soudjani S., Majumdar R. Concentration of measure for chance-constrained optimization // IFAC-PapersOnLine. 2018. V. 51. No. 16. P. 277–282.
  20. Lejeune M., Prekopa A. Relaxations for probabilistically constrained stochastic programming problems: Review and extensions // Annals of Operations Research. 2018. P. 1–22.
  21. Campi M., Garatti S. A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality // J. Optim. Theory Appl. 2011. V. 148. No. 2. P. 257–280.
  22. Alamo T., Mirasierra V., Dabbene F., Lorenzzen M. Safe approximations of chance constrained sets by probabilistic scaling // 2019 18th European Control Conference (ECC). IEEE, 2019. P. 1380–1385.
  23. Alamo T., Tempo R., Luque A., Ramirez D. Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms // Automatica. 2015. V. 52. P. 160–172.
  24. Lorenzen M., Dabbene F., Tempo R., Allgower F. Stochastic MPC with offline uncertainty sampling // Automatica. 2017. V. 81. P. 176–183.
  25. Mammarella M., Lorenzzen M., Capello E., Park H., Dabbene F., Guglieri G., Romano M., Allgower F. An offline-sampling SMPC framework with application to autonomous space maneuvers // IEEE Transactions on Control Systems Technology. 2018. V. 28. No. 2. P. 388–402.
  26. Calaftore G. Random convex programs // SIAM J. Optim. 2010. V. 20. No. 6. P. 3427–3464.
  27. Vapnik V. The Nature of Statistical Learning Theory. New York: Springer Science & Business Media, 1999.
  28. Alamo T., Tempo R., Camacho E. Randomized strategies for probabilistic solutions of uncertain feasibility and optimization problems // IEEE Transactions on Automatic Control. 2009. V. 54. No. 11. P. 2545–2559.
  29. Alamo T., Tempo R., Camacho E. Improved sample size bounds for probabilistic robust control design: A pack-based strategy // 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. P. 6178–6183.
  30. Alamo T., Manzano J., Camacho E. Robust design through probabilistic maximization / Uncertainty in Complex Networked Systems. Springer, 2018. P. 247–274.
  31. Nievergelt J. Exhaustive search, combinatorial optimization and enumeration: Exploring the potential of raw computing power // International Conference on Current Trends in Theory and Practice of Computer Science. Springer, 2000. P. 18–35.
  32. Lukashevich A., Gorchakov V., Vorobev P., Deka D., Maximov Y. Importance sampling approach to chance-constrained DC optimal power flow // IEEE Transactions on Control of Network Systems. 2023. V. 11. No. 2. P. 928–937.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу

© The Russian Academy of Sciences, 2025