Optimal Retention of the Trajectories of a Discrete-Time Stochastic System in a Tube: One Problem Statement

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Resumo

This paper considers an optimal control problem for a time-invariant linear stochastic system with discrete time, scalar unbounded control, additive noise, and a probabilistic criterion for retaining its trajectories in a given neighborhood of zero. We use dynamic programming and two-sided Bellman function estimates to derive analytical expressions for the optimal control at two time steps and a suboptimal control on any control horizon. The effectiveness of these controls is illustrated on a numerical example.

Sobre autores

A. Tarasov

Moscow Aviation Institute

Email: tarrapid@gmail.com
Moscow, Russia

V. Azanov

Moscow Aviation Institute

Email: azanov59@gmail.com
Moscow, Russia

A. Kibzun

Moscow Aviation Institute

Autor responsável pela correspondência
Email: kibzun@mail.ru
Moscow, Russia

Bibliografia

  1. Малышев В.В., Кибзун А.И. Анализ и синтез высокоточного управления летательными аппаратами. М.: Машиностроение, 1987.
  2. Lesser K., Oishi M., Erwin R. Stochastic reachability for control of spacecraft relative motion // Proc. IEEE Conf. Dec. and Ctrl. 2013. P. 4705-4712.
  3. Kan Y.S. Control Optimization by the Quantile Criterion // Autom. Remote Control. 2001. V. 62. No. 6. P. 746-757.
  4. Azanov V.M., Kan Yu.S. Design of Optimal Strategies in the Problems of Discrete System Control by the Probabilistic Criterion // Autom. Remote Control. 2017. V. 78. No. 6. P. 1006-1027.
  5. Кузьмин В.П., Ярошевский В.А. Оценка предельных отклонений фазовых координат динамической системы при случайных возмущениях. М.: Наука, 1995.
  6. Soudjani S., Abate A. Probabilistic reach-avoid computation for partially degenerate stochastic processes // IEEE Trans. Autom. Ctrl. IEEE Trans. Autom. Ctrl., 2014. V. 59. No. 2. P. 528-534.
  7. Summers S., Lygeros J. Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem // Automatica. 2010. V. 46. No. 12. P. 1951-1961.
  8. Vinod A., Oishi M. Scalable underapproximation for the stochastic reach-avoid problem for highdimensional LTI systems using Fourier transforms // IEEE Lett.-Contr. Syst. Soc. 2017. V. 1. No. 2. P. 316-321.
  9. Jasour A.M., Aybat N.S., Lagoa C.M. Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets // SIAM J. Optimization. 2015. V. 25. No. 3. P. 1411-1440.
  10. Jasour A.M., Lagoa C.M. Convex constrained semialgebraic volume optimization: Application in systems and control. arXiv:1701.08910, 2017.
  11. Grigor'ev P.V., Kan Y.S Optimal Control of the Investment Portfolio with Respect to the Quantile Criterion // Autom. Remote Control. 2004. V. 65. No. 2. P. 319-336.
  12. Bunto T.V., Kan Y.S. Quantile criterion-based control of the securities portfolio with a nonzero ruin probability // Autom. Remote Control. 2013. V. 74. No. 5. P. 811-828.
  13. Maidens J.N., Kaynama S., Mitchell I.M., Oishi M.M., Dumont G.A. Lagrangian methods for approximating the viability kernelin high-dimensional systems // Automatica. 2013. V. 49. No. 7. P. 2017-2029.
  14. Kariotoglou N., Raimondo D.M., Summers S., Lygeros J. Astochastic reachability framework for autonomous surveillance withpan-tilt-zoom cameras // Proc. European Ctrl. Conf. 2011. P. 1411-1416.
  15. Doyen L., De Lara M. Stochastic viability and dynamic programming // Systems and Control Letters. 2010. V. 59. No. 10. P. 629-634.
  16. Кибзун А.И., Иванов С.В., Степанова А.С. Построение доверительного множества поглощения в задачах анализа статических стохастических систем // АиТ. 2020. № 4. С. 21-36.
  17. Azanov V.M., Kan Yu.S. Bilateral Estimation of the Bellman Function in the Problems of Optimal Stochastic Control of Discrete Systems by the Probabilistic Performance Criterion // Autom. Remote Control. 2018. V. 79. No. 2. P. 203-215.
  18. Azanov V.M., Kan Yu.S. Refined Estimation of the Bellman Function for Stochastic Optimal Control Problems with Probabilistic Performance Criterion // Autom. Remote Control. 2019. V. 90. No. 4. P. 634-647.
  19. Vinod A.P., Oishi M.M. Stochastic reachability of a target tube: Theory and computation // Automatica. 2021. V. 125.
  20. Афанасьев В.Н., Колмановский В.Б., Носов В.Р. Математическая теория конструирования систем управления. М.: Высш. шк., 2003.
  21. Azanov V.M., Tarasov A.N. Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function // Autom. Remote Control. 2020. V. 81. P. 1819-1839.
  22. Konrad Schmudgen. The moment problem. Vol. 9. Springer, 2017.
  23. Azanov V.M., Kan Yu.S. On Optimal Retention of the Trajectory of Discrete Stochastic System in Tube // Autom. Remote Control. 2019. V. 80. No. 1. P. 30-42.
  24. Кан Ю.С., Кибзун А.И. Задачи стохастического программирования с вероятностными критериями. М.: ФИЗМАТЛИТ, 2009.

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