Abstract
Suboptimal solutions of nonlinear optimal control problems are addressed in the present work. These suboptimal approaches are known as Approximating Sequence of Riccati Equations (ASRE) methods. In the ASRE methods, the nonlinear problem is reduced to a sequence of linear-quadratic and time-varying approximating problems. For this purpose, the nonlinear equations are written in State Dependent Coefficient (SDC) factorization form. Two different ASRE approaches are discussed and their implementation procedures will be explained. To implement and compare these two techniques, spacecraft Coulomb formations are considered. Suboptimal trajectories of formation attitude and relative position of a two-craft formation utilizing coulomb forces as well as thrusters is discussed. The effectiveness of the approaches as well as their comparison is demonstrated through numerical simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berryman, J., Schaub, H.: Static equilibrium configurations in geo Coulomb spacecraft formations. In: Paper AAS 05-104, AAS/AIAA Space Flight Mechanics Meeting, Copper Mountain (2005)
Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Guid. Control Dyn. 21, 193–207 (1998)
Bogdanov, A., Wan, E.A.: State-dependent riccati equation control for small autonomous helicopters. J. Guid. Control Dyn. 30, 47–60 (2007)
Bracci, A., Innocenti, M., Pollini, L.: Estimation of the region of attraction for state-dependent riccati equation controllers. J. Guid. Control Dyn 29, 1427–1430 (2006)
Bryson, A.E., Ho, Y.C.: Applied Optimal Control, pp. 65–69, 150–151. Wiley, New York (1975)
Çimen, T.: Survey of state-dependent riccati equation in nonlinear optimal feedback control synthesis. J. Guid. Control Dyn. 35, 1025–1047 (2012)
Çimen, T., Banks, S.P.: Global optimal feedback control for general non linear system with non-quadratic performance criteria. Syst. Control Lett. 53, 327–346 (2004a)
Çimen, T., Banks, S.P.: Global optimal feedback control for general non linear system with non-quadratic performance criteria. Automatica 40, 1845–1863 (2004b)
Cloutier, R., D’Souza, C.A., Mracek, C.P.: Nonlinear regulation and nonlinear h-infinity control via the state-dependent riccati equation technique: part 1, theory; part 2, examples, pp. 117–141. In: Proceedings of the First International Conference on Nonlinear Problems in Aviation and Aerospace (1996)
Conway, B.: Spacecraft Trajectory Optimization, pp. 37–78. Cambridge University Press, Cambridge (2010)
Gomroki, M.M., Tekinalp, O.: Relative position control of a two-satellite formation using the SDRE control method. In: Paper AAS 14-217, 24th AAS/AIAA SpaceFlight Mechanics Meeting, pp. 235–254, Santa Fe, 26–30 January 2014a
Gomroki, M. M., Tekinalp, O.: Maneuvering of two-craft coulomb formation using ASRE method. In: Paper AIAA 2014-4164, AIAA/AAS Astrodynamics Specialist Conference, San Diego, 4–7 August 2014b
Harman, R.R., Bar-Itzhack, I.Y.: Pseudolinear and state-dependent riccati equation filters for angular rate estimation. J. Guid. Control Dyn. 22, 723–725 (1999)
Kim, C.-J., Park, S.H., Sung, S.K., Jung, S.-N.: Nonlinear optimal control analysis using state-dependent matrix exponential and its integrals. J. Guid. Control Dyn 32, 309–313 (2009)
Mracek, C.P., Cloutier, J.R.: Control designs for the nonlinear benchmark problem via the state-dependent riccati equation method. Int. J. Robust Nonlinear Control 8, 401–433 (1998)
Mullen, E.G., Gussenhoven, M.S., Hardy, D.A.: SCATHA survey of high-voltage spacecraft charging in sunlight. J. Geophys. Sci. 91, 1074–1090 (1986)
Pearson, J.D.: Approximation methods in optimal control. J. Electron. Control 13, 453–469 (1962)
Ratnoo, A., Ghose, D.: Study of interspacecraft coulomb forces and implications for formation flying. J. Propuls. Power 19, 497–505 (2003)
Ratnoo, A., Ghose, D.: State-dependent riccati-equation-based guidance law for impact-angle-constrained trajectories. J. Guid. Control Dyn. 32, 320–325 (2009)
Schaub, H., Kim, M.: Orbit element difference constraints for Coulomb satellite formations. In: Paper AIAA 04-5213, AIAA/AAS Astrodynamics Specialist Conference, Providence (2004)
Topputo, F., Bernelli-Zazzera, F.: A method to solve nonlinear optimal control problems in astrodynamics. Adv. Astronaut. Sci. 145, 1531–1544 (2012)
Topputo, F., Bernelli-Zazzera, F.: Approximate solutions to nonlinear optimal control problems in astrodynamic. ISRN Aerosp. Eng. 2013, 1–7 (2013)
Wernli, A., Cook, G.: Suboptimal control for the nonlinear quadratic regulator problem. Automatica 11, 75–84 (1975)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Gomroki, M.M., Topputo, F., Tekinalp, O., Bernelli-Zazzera, F. (2016). Two ASRE Approaches with Application to Spacecraft Coulomb Formations. In: Gómez, G., Masdemont, J. (eds) Astrodynamics Network AstroNet-II. Astrophysics and Space Science Proceedings, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-23986-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-23986-6_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23984-2
Online ISBN: 978-3-319-23986-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)