Disturbed motion of a hypersonic vehicle in climb


Disturbed motion of a hypersonic vehicle in climb is analyzed. Deviations of atmospheric density from standard values and deviations of aerodynamic force coefficients from nominal values are taken as disturbances. Disturbed motion of a hypersonic vehicle with the optimum angle-of-attack schedule and nominal flight characteristics is modeled. Deviations of terminal conditions of disturbed motion from the target values of velocity, altitude and path inclination are determined. Using the method of Pontryagin’s maximum principle the problem of fuel mass minimum consumed in hypersonic acceleration climb is solved for disturbed motion. Optimal angle-of-attack schedules, optimal flight paths and finite values of the hypersonic vehicle’s mass are determined. Comparative analysis of optimal control programs and flight paths obtained for disturbed and undisturbed motion is carried out.

About the authors

V. L. Balakin

Samara National Research University

Author for correspondence.
Email: balakin.vl@ssau.ru

Doctor of Science (Engineering), Professor
University Administration Counselor

Russian Federation

M. M. Krikunov

Samara National Research University

Email: krikunov.mm@ssau.ru

Candidate of Science (Engineering)
Senior Research Associate

Russian Federation


  1. Balakin V.L., Krikunov M.M. Analysis of control programs and flight paths of a hypersonic vehicle in climb. Vestnik of Samara University. Aerospace and Mechanical Engineering. 2018. V. 17, no. 4. P. 18-26. doi: 10.18287/2541-7533-2018-17-4-18-26 (In Russ.)
  2. Buzuluk V.I. Optimizatsiya traektoriy dvizheniya aerokosmicheskikh letatel'nykh apparatov [Optimization of aerospace vehicle flight paths]. Moscow: Central Aerohydrodynamic Institute Publ., 2008. 476 p.
  3. Nechaev Yu.N. Silovye ustanovki giperzvukovykh i vozdushno-kosmicheskikh letatel'nykh apparatov [Power units of hypersonic and space-air vehicles]. Moscow: Rossiyskaya Akademiya Kosmonavtiki Publ., 1996. 214 p.
  4. Nechaev Yu.N., Polev A.S., Nikulin A.V. Modelirovanie usloviy raboty parovodorodnogo RTD v sostave silovoy ustanovki giperzvukovogo letatel'nogo apparata. Vestnik Akademii kosmonavtiki. Nauchno-tekhnicheskie problemy kosmonavtiki. Vypusk 2. Materialy nauchnykh dokladov na zasedaniyakh napravleniya v 1996-1997 gg. Moscow: Rossiyskaya Akademiya Kosmonavtiki Publ., 1998. P. 159-191. (In Russ.)
  5. Bebyakov A.A. Optimal control of the angle of attack of a hypersonic flight vehicle. Vestnik of the Samara State Aerospace University. 2013. No. 1 (39). P. 26-38. doi: 10.18287/1998-6629-2013-0-1(39)-26-38 (In Russ.)
  6. Shkol'nyy E.P., Mayboroda A. Atmosfera i upravlenie dvizheniem letatel'nykh apparatov [Atmosphere and aircraft motion control]. Leningrad: Gidrometeoizdat Publ., 1973. 308 p.
  7. Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimal'nykh protsessov [Mathematical theory of optimal processes]. Moscow: Nauka Publ., 1983. 393 p.



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