ON THE PROPERTIES OF THE SOLVABILITY SET FOR A LINEAR SYSTEM WITH UNCERTAINTY

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

The work is devoted to the problem of verifying that the state of a linear controlled system of differential equations will hit the target set over a finite time interval, despite the uncertainties (noise). Some geometric, pointwise convex constraints on uncertainties are imposed. In the case of a two-dimensional state space a method is proposed for constructing a solvability set without the calculation of the convex hulls of the functions necessary to construct a support function of the geometric difference of the sets. A Hamilton–Jacobi–Bellman type equation is obtained, which is satisfied by the distance function to the solvability set.

作者简介

A. Melnikova

Lomonosov Moscow State University;

Email: nastya.a.melnikova@gmail.com

P. Tochilin

Lomonosov Moscow State University; V.A. Trapeznikov Institute of Control Sciences of RAS

Email: tochilin@cs.msu.ru

A. Daryin

Lomonosov Moscow State University

Email: daryin@mail.ru

参考

  1. Pontriagin, L.S., On linear differential games. II, Dokl. Akad. Nauk SSSR, 1967, vol. 175, no. 4, pp. 910–912.
  2. Pontriagin, L.S., Linear differential games of pursuit, Math. USSR-Sb., 1981, vol. 40, no. 3, pp. 285–303.
  3. Kurzhanski, A.B., Pontryagin’s alternated integral in the theory of control synthesis, Proc. Steklov Inst. Math.,1999, vol. 224, pp. 212–225.
  4. Kurzhanski, A.B. Dynamics and Control of Trajectory Tubes / A.B. Kurzhanski, P. Varaiya. — Basel : Birkhauser, 2014. — 445 p.
  5. Fleming W.H. Controlled Markov Processes and Viscosity Solutions / W.H. Fleming, H.M. Soner. — New York : Springer, 2006. — 429 p.
  6. Melnikova, A.A. and Tochilin, P.A., On a problem of calculating the solvability set for a linear system with uncertainty, Differ. Equat., 2023, vol. 59, no. 11, pp. 1538–1546.
  7. Kurzhanski, A.B. Ellipsoidal Calculus for Estimation and Control / A.B. Kurzhanski, I. Valyi. — Boston : Birkhauser, 1997. — 321 p.
  8. Polovinkin, E.S. and Balashov, M.V., Elementy vypuklogo i sil’no vypuklogo analiza (Elements of Convex and Strongly Convex Analysis), Moscow: Fizmatlit, 2007.
  9. Kurzhanski, A.B., Upravlenie i nabl’udenie v usloviah neopedelennosti (Control and Observation under Uncertainty Conditions), Moscow: Nauka, 1977.
  10. Rockafellar, R.T., Convex Analysis, Princeton: Princeton Univ. Press, 1970.
  11. Arutyunov, A.V., Lekcii po vypuklomu i mnogoznachnomu analizu (Lectures on Convex and Set-Valued Analysis), Moscow: Fizmatlit, 2014
  12. Filippov, A.F., Differential Equations with Discontinuous Righthand Sides, Springer, 1988.
  13. Lyapunov, A.A., On countably additive set-functions, Izv. Akad. Nauk SSSR Ser. Mat., 1940, no. 6, pp. 465–478

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2024