On State Estimation for Multi-Agent Motion: Discrete-Time Systems
DOI:
https://doi.org/10.14529/cmse160102Keywords:
reachable sets, discrete-time systems, multi-agent motion, polyhedral estimatesAbstract
The reachability problem for linear discrete-time control systems which describe multi-agent motion is considered. Namely, we consider a finite set of subsystems with controls to be chosen under the condition that the trajectories of the subsystems are pairwise not very close to and not very far away from each other. Properties of reachable sets of such systems are described. Some algorithms for constructing external polyhedral (parallelepiped-valued) estimates for reachable sets are proposed.
References
Гусев, М.И. Внешние оценки множеств достижимости нелинейных управляемых систем / М.И. Гусев // Автоматика и телемеханика. --- 2012. --- № 3. --- С. 39--51.
Костоусова, Е.К. Параллельные вычисления при оценивании областей достижимости и информационных множеств линейных систем / Е.К. Костоусова // Алгоритмы и программные средства параллельных вычислений.
--- Екатеринбург: УрО РАН, 1999. --- Вып.3. --- С. 107--126.
Куржанский, А.Б. Задача управления групповым движением. Общие соотношения / А.Б. Куржанский // Докл. РАН. --- 2009. --- Т. 426, № 1. --- С. 20--25.
Черноусько, Ф.Л. Оценивание фазового состояния динамических систем. Метод эллипсоидов / Ф.Л. Черноусько.
--- М.: Наука, 1988. --- 319 с.
Filippova, T.F. Approximation techniques in impulsive control problems for the tubes of solutions of uncertain differential systems
/ T.F. Filippova // Springer Proc. Mathematics and Statistics.
--- 2013. --- Vol. 41. -- P. 385--396.
Kostousova, E.K. State estimation for dynamic systems via parallelotopes: optimization and parallel computations / E.K. Kostousova // Optimiz. Methods & Software. --- 1998. --- Vol. 9, No. 14. --- P. 269--306.
Kurzhanski, A.B. Ellipsoidal Calculus for Estimation and Control
/ A.B.Kurzhanski, I.V'alyi. --- Boston: Birk-h"a-u-ser, 1997. --- 321 p.
Kurzhanski, A.B. On synthesizing team target controls under obstacles and collision avoidance / A.B. Kurzhanski, P. Varaiya
// J. Franklin Inst. --- 2010. --- Vol. 347, No. 1. --- P. 130--145.
Kurzhanski, A.B. Dynamics and Control of Trajectory Tubes: Theory and Computation. (Systems & Control: Foundations & Applications, Book 85) / A.B. Kurzhanski, P. Varaiya
--- Birk-h"a-u-ser Basel, 2014. --- 445 p.
Olfati-Saber, R. Flocking for multi-agent dynamic systems: algorithms and theory / R. Olfati-Saber // IEEE Trans. on Automatic Control. --- 2006. --- Vol. 51, No. 3. --- P. 401--420.
Vicino, A. Sequential approximation of feasible parameter sets
for identification with set membership uncertainty / A. Vicino, G. Zappa // IEEE Trans. Automat. Contr. --- 1996. --- Vol. 41, No. 6. --- P. 774--785.


