Skip to main content
SpringerLink
Log in

Estimate of the control threshold value in the problem on a time-optimal satellite attitude transition maneuver

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The time-optimal problem is considered for a nonlinear Lagrangian system with one degree of freedom. The system is controlled by a force bounded in absolute value, and all noncontrol forces are potential.We study the properties of optimal synthesis on the phase cylinder and indicate the conditions under which it has the simplest structure, namely, involves at most one switching for any initial conditions. The approach is used to specify the structure of the well-known solution in the classical problem on the time-optimal satellite attitude transition maneuver in the orbit plane.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. V. Beletskii, “Optimal Transfer of an Earth Satellite to a Gravitationally Stable Position,” Kosmich. Isseld. 9 (3), 366–375 (1971) [Cosmic Res. (Engl. Transl.) 9 (3), 337–344 (1971)].

    ADS  Google Scholar 

  2. A. A. Anchev, “Equilibrium Attitude Transitions of a Three-Rotor Gyrostat in a Circular Orbit,” AIAA J. 11 (4), 467–472 (1973).

    Article  ADS  MATH  Google Scholar 

  3. A. P. Markeev, Theoretical Mechanics (NITs “Regular and Chaotic Dynamics,” Moscow–Izhevsk, 2007) [in Russian].

    MATH  Google Scholar 

  4. S. A. Reshmin and F. L. Chernous’ko, “A Time-Optimal Control Synthesis for a Nonlinear Pendulum,” Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 1, 13–22 (2007) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 46 (1), 9–18 (2007)].

    MATH  Google Scholar 

  5. S. A. Reshmin, “Finding the Principal Bifurcation Value of the Maximum Control Torque in the Problem of Optimal Control Synthesis for a Pendulum,” Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 2, 5–20 (2008) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 47 (2), 163–178 (2008)].

    MathSciNet  MATH  Google Scholar 

  6. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Gordon & Breach Sci. Publ., New York, 1986).

    Google Scholar 

  7. R. Isaacs, Differential Games (Wiley, New York, 1965; Mir, Moscow, 1967).

    MATH  Google Scholar 

  8. E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Wiley, New York, 1967; Nauka, Moscow, 1972).

    MATH  Google Scholar 

  9. B. Friedland and P. Sarachik, “Indifference Regions in Optimum Attitude Control,” IEEE Trans. Automatic Control 9 (2), 180–181 (1964).

    Article  Google Scholar 

  10. J. L. Garcia Almuzara and I. Flügge-Lotz, “Minimum Time Control of a Nonlinear System,” J. Differen. Equations 4 (1), 12–39 (1968).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. S. A. Reshmin, “Bifurcation in a Time-Optimal Problem for a Second-Order Non-Linear System,” Prikl. Mat. Mekh. 73 (4), 562–572 (2009) [J. Appl. Math. Mech. (Engl. Transl.) 73 (4), 403–410 (2009)].

    MathSciNet  MATH  Google Scholar 

  12. S. A. Reshmin and F. L. Chernousko, “Properties of the Time-Optimal Feedback Control for a Pendulum-Like System,” J. Optimiz. Theory Appl. 163 (1), 320–252 (2014).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526, Russia

    S. A. Reshmin

  2. Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, Moscow, 105005, Russia

    S. A. Reshmin

Authors
  1. S. A. Reshmin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Reshmin.

Additional information

Original Russian Text © S.A. Reshmin, 2017, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2017, No. 1, pp. 12–22.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reshmin, S.A. Estimate of the control threshold value in the problem on a time-optimal satellite attitude transition maneuver. Mech. Solids 52, 9–17 (2017). https://doi.org/10.3103/S0025654417010022

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654417010022

Keywords

Search

Navigation