Scholarly record
EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT
Abstract
Satellite motion control in the vicinity of the libration point with expenditure criteria is considered. Expenditure optimization is natural in the case, where it is necessary to keep mechanical system in the neighborhood of the equilibrium point for a long time. Disturbing factors from time to time distort this system unacceptably far from the equilibrium point, and we need to extinguish these deviations, using fuel or another resource, which reserves are limited. Optimization of the satellite motion control according to this criterion is important not only from the economic and technical side, but also brings an environmental effect. Features of the presented mathematical problem definition are following. While deviations from the equilibrium point are very small, its controlled motion can be by linear differential equations with constant coefficients. The admissible control is a piecewise polynomial function that blanks selected frequency components of the solution of linear equations at the terminated moment T. As the expenditure functional we use the integral of the sum of the control coordinates modules along the interval [0,T]. As the results of solving the problem, formulas and an algorithm for finding the control switching points satisfying the expenditure functional extremum necessary conditions are proposed.
Publication Impact Profile
- Captures
- Mendeley - Readers: 1
Publication details
References8
Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Control with Expenditure Criteria in Rotational Motion of the Satellite Moving along a Circular Orbit, Greece, AIP Conference Proceeding Vol.1648, American Institute of Physics, 2015, pp.1-4. DOI: 10.1063/1.4912669
Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Expenditure Optimization in a Problem of Controlled Motion of Mechanical Systems, Greece, AIP Conference Proceeding Vol.1738, American Institute of Physics, 2016, pp.1-4. DOI: 10.1063/1.4951941
Alesova I.M., Babadzanjanz L.K., Pototskaya I.Yu., Pupysheva Yu.Yu., Saakyan A.T., Piecewise polynomial control in mechanical systems, Greece, AIP Conference Proceeding Vol. 1863, American Institute of Physics, 2017, pp.1-4. DOI: 10.1063/1.4992352
Alesova I.M., Babadzanjanz L.K., Bregman A.M., Bregman K.M., Pototskaya I.Yu., Pupysheva Yu.Yu., Saakyan A.T., Piecewise constant control of linear mechanical systems in the general case, Greece, AIP Conference Proceeding Vol. 1978, American Institute of Physics, 2018, pp.1-4. DOI: 10.1063/1.5043753
Farquhar, R.W., Dunham, D.W. Use of Libration-Point Orbits for Space Observatories. In: Kondo, Y. (eds) Observatories in Earth Orbit and Beyond. Astrophysics and Space Science Library, vol 166. Springer, Dordrecht, 1990. DOI: 10.1007/978-94-011-3454-5_52
Szebehely Victor, Theory of Orbits, Academic Press, New York, 1967.
Ardaens J.S., D�Amico S. Control of formation flying spacecraft at a Lagrange point. DLR, 2008.
Markeev A.P. Tochki libratsii v nebesnoy mekhanike i kosmodinamike [Vibration points in celestial mechanics and cosmodynamics]. Moscow, Nauka Publ., 1978 (in Russ.).
View or Download full articleAccess options
SWS access login
Login as SWS Scientific CommitteeLogin as SWS Scientific PartnerLogin as SWS AuthorAuthors and approved SWS contributors will read and export their own linked papers after identity matching by SWS profile, email and SGEM GlobalID.
For librarian assistance: [email protected]
Purchase Instant Access
- Article can be downloaded after successful payment.
- Article may be used according to SWS library access terms.
- Article cannot be redistributed.