Fastest Satellite Orbit Correction with Limited Summary Fuel Supply

Аuthors

Ibragimov D. N.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: rikk.dan@gmail.com

Keywords:

satellite orbit correction, circular orbit, time-optimization problem, discrete-time linear system, null-controllable set, summary control constraints

References

1. 1.Ivanov S.G., Grishko D.A., Baranov A.A. Change of perigee argument of medium Earth orbit with constant semi-major axis and different eccentricity. Trudy MAI. 2024. No. 139. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=183447
2. 2.Vas'kova V.S. On the motion of a spacecraft along a tether by non-perfect solar sail. Trudy MAI. 2024. No. 139. (In Russ.). URL: https://trudymai.ru/ eng/published.php?ID=1834499
3. 3.Minakov E.P., Aleksandrov M.A., Mishcheryakov A.V., Mishcheryakov S.V. Algorithm for determining the parameters of oblinated projections of points on the earth's surface for circular orbits of space vehicles. Trudy MAI. 2024. No. 135. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=179696&eng=Y
4. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko B.F. Matematicheskaya teoriya optimal'nykh protsessov (Mathematical theory of the optimal processes). Moscow: Nauka Publ, 1969. 393 p.
5. Boltyanskii V.G. Optimal'noe upravlenie diskretnymi sistemami (Optimal control of discrete-time systems). Moscow: Nauka Publ, 1973. 448 p.
6. Propoi A.I. Elementy teorii optimal'nykh diskretnykh protsessov (Elements of the theory of the optimal discrete-time processes). Moscow: Nauka Publ, 1973. 255 p.
7. Desoer C.A., Wing J. The Minimal Time Regulator Problem for Linear Sampled-Data Systems: General Theory. Journal Franklin Institute. 1961. V. 272, No. 3. P. 208–228.
8. Lin W.-S. Time-Optimal Control Strategy for Saturating Linear Discrete Systems. International Journal of Control. 1986. V. 43, No. 5. P. 1343–1351. DOI: 10.1080/00207178608933543
9. Moroz A.I. Synthesis of Time-Optimal Control for Linear Discrete Objects of the Third Order. Avtomatika i telemekhanika. 1965. No.2. P. 193–207. (In Russ.)
10. Krasnoshchechenko V.I. Simplex Method for Solving the Brachistochrone Problem at State and Control Constraints. Inzhenernyj zhurnal: nauka i innovanii. 2014. No. 6. (In Russ.). URL: http://engjournal.ru/catalog/it/asu/1252.html
11. Cazanova L.A. Stability of Optimal Synthesis in the Time-Optimization Problem. Izvestiya vuzov. Matematika. 2002. No. 2. P. 46–57. (In Russ.)
12. Bortakovskii A.S. Speed of Performance of a Group of Controlled Objects Izvestiya RAN. Teoriya i sistemy upravleniya. 2023. No. 5. P. 16–42. (In Russ.). DOI: 10.31857/S0002338823050049
13. Chen D., Bako L., Lecoeuche S. The Minimum-Time Problem for Discrete-Time Linear Systems: A Non-Smooth Optimization Approach. Proceedings of the IEEE International Conference on Control Applications. 2012. P. 196–201. DOI:10.1109/CCA.2012.6402693
14. Abdelhak A., Rachik M. The Linear Quadratic Minimum-Time Problem for a Class of Discrete Systems. Journal of Mathematical Programming and Operations Research. 2010. V. 59, No. 4. P. 575–587. DOI: 10.1080/02331930801954672
15. Lee J., Haddad W.M. Fixed Time Stability and Optimal Stabilisation of Discrete Autonomous Systems. International Journal of Control. 2022. V. 96, No. 9. P. 2341–2355. DOI: 10.1080/00207179.2022.2092557
16. Ibragimov D.N. On the Optimal Speed Problem for the Class of Linear Autonomous Infinite-Dimensional Discrete-Time Systems with Bounded Control and Degenerate Operator. Avtomatika i telemekhanika. 2019. No. 3. P. 3–25. (In Russ.). DOI: 10.1134/S0005231019030012
17. Ibragimov D.N., Novozhilkin N.M., Portseva E.Yu. On Sufficient Optimality Conditions for a Guaranteed Control in the Speed Problem for a Linear Time-Varying Discrete-Time System with Bounded Control. Avtomatika i telemekhanika. 2021. No. 12. P. 48–72. (In Russ.). DOI: 10.31857/S0005231021120047
18. Kamenev G.K. Chislennoe issledovanie effektivnosti metodov poliedral'noi approksimatsii vypuklykh tel (Numerical study of the efficiency of polyhedral approximation methods for convex bodies). Moscow: Vychislitel'nyi tsentr RAN Publ., 2010. 119 p.
19. Kozorez D.A., Krasil'shchikov M.N., Kruzhkov D.M., Sypalo K.I. Integrated Navigation System for a Space Vehicle on a Geostationary or Highly Elliptic Orbit Operating in the Presence of Active Jam. Izvestiya RAN. Teoriya i sistemy upravleniya. 2013. No. 3. P. 143–154. (In Russ.)
20. Malyshev V.V., Krasil'shchikov M.N., Bobronnikov V.T. Sputnikovye sistemy monitoringa. Analiz, sintez i upravlenie (Satellite monitoring systems. Analysis, synthesis and control). Moscow: MAI Publ., 2000. 568 p.
21. Ibragimov D.N., Sirotin A.N. On Some Properties of Sets of Bounded Controllability for Stationary Linear Discrete Systems with Total Control Constraints. Izvestiya RAN. Teoriya i sistemy upravleniya. 2023. No. 6. P. 3–32. (In Russ.). DOI: 10.31857/S0002338823050086
22. Ibragimov D.N. On the Method for Constructing Null-Controllable Sets for Linear Discrete-Time Systems with Summary Control Constraints. Mekhatronika, avtomatizatsiya, upravlenie. 2024. V. 25, No. 10. P. 503–512. (In Russ.)
23. Rokafellar R. Vypuklyi analiz (Convex Analysis). Moscow: Mir Publ., 1973. 469 p.
24. Kolmogorov A.N., Fomin S.V. Elementy teorii funktsii i funktsional'nogo analiza (Elements of the theory of functions and functional analysis). Moscow: Fizmatlit Publ., 2009. 509 p.

Download