• Marta M. Komnatska
  • Anatoliy A. Tunik



fuzzy optimization, fuzzy robust control, model with parameters un certainties, linear matrix inequality


 This paper deals with combination of two powerful and modern control tools as linear matrix inequality that is used for synthesis a ‘crisp’ controller and a fuzzy control approach for designing a soft controller. The control design consists of two stages. The first stage investigates the problem of a robust an controller design with parameters uncertainties of the handled plant in the presence of external disturbances. Stability conditions are obtained via a quadratic Lyapunov function and represented in the form of linear matrix inequalities. The second stage consists of the outer loop controller construction based on fuzzy inference system that utilizes for altitude hold mode. The parameters of the fuzzy controller are adjusted with a gradient descent method in order to improve the performance of the overall system. The case study illustrates the efficiency of the proposed approach to the flight control of small Unmanned Aerial Vehicle

Author Biographies

Marta M. Komnatska

Post-gaduate student National Aviation University.

Anatoliy A. Tunik

Doctor of Engineering. Professor National Aviation University.


Tunik A.A. Robust Stabilization and Nominal Performance of the Flight Control System for Small UAV / A.A. Tunik, T.A. Galaguz // Applied and computation mathematics.– 2004. – Vol. 3, № 1.– P. 34–45.

Оптимальне управління боковим каналом БПЛА при неповних вимірах вектора стану / А.А. Тунік, Т.А. Галагаз, М.М. Комнацька, Т.А. Білий // Проблеми інформатизації та управління. – 2005. – № 12.– С. 143–146.

Tanaka K. Fuzzy Control System Design and Analysis. A Linear Matrix Inequality Approach / K. Tanaka, H.O. Wang. – New York.: John Wiley& Sons, Inc,2001. – 305 p.

Boyd S. Linear Matrix Inequalities in System and Control Theory / S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan. – Philadelphia, PA SIAM, 1994. – 416 p.

Grman L. Robust Output Feedback Quadratic Controller Design / L. Grman, V. Veselý // Journal of Electrical Engineering. – 2005. – Vol. 56.–P. 128–134.

Ларин В.Б. О компенсации внешних возмущений динамической обратной связью по выходной переменной / В.Б. Ларин, А.А. Туник // Прикладная механіка.– 2006.– Т. 42, №5.– С. 132 –144.

Feng J. Quadratic Stabilization for Uncertain Stochastic Systems / J. Feng, W. Zhang // Journal of Control Theory and Applications. – 2005. – № 3. – P. 252–258.

Output Feedback LMI Tracking Control Conditions with criterion for Uncertain and Disturbed T-S models / B. Mansouri, N. Manamanni, K. Guelton, et al // Information Sciences. – (179) 2009. – P. 446−457.

An LMI Approach To Robust Control For Uncertain Continuous- Time Systems / S.-W. Kau, Y.-S. Liu, C.-H. Lee, et al // Asian Journal of Control.–June 2005. – Vol. 7, No. 2. – P. 182–186.

Xie L. Control and Quadratic Stabilization of Systems with Parameter Uncertainty Via Output Feedback / L. Xie // IEEE Trans. Automat. Contr. – Vol. 37, No. 8. – P. 1253–1256.

Zhou K. Robust Stabilization of Linear Systems with Norm – Bounded Timevarying Uncertainty / K. Zhou, P. Khargonekar // Systems and Control Letters. – 1998. – № 10 (1). – P. 17–20.

Passino, K.M., Fuzzy Control / K.M Passino, S. Yurkovich.–Addison–Wesley.– Menlo Park, Reading, Harlow, Berkley, Sidney, Bonn, Amsterdam, 1998. – 502 p.

Simon D. Sum Normal Optimization of Fuzzy Membership Functions / D. Simon // International Journal of Uncertainty, Fuzziness and Knowledge – Based Systems. – 2002. – Vol.10. − P.363−384.

McLean D. Automatic Flight Control Systems / D. McLean. Prentice Hall Inc., Englewood Cliffs. – 1990.– 593 p.

Ruaw M.A. Simulink toolbox for Flight Dynamic and Control / M.A. Ruaw. TUDelft, Delft university of Technology. – 2005. – 253 p.

Layne J. R. Fuzzy Model Reference Learning Control / J. R. Layne, K.M. Passino // Journal of Intelligent and Fuzzy Systems.–1996. –Vol. 4, No. 1, P. 33–47.

Tunik A.A. Combination of fuzzy and crisp control in airborne robust multivariable systems / A.A. Tunik, M.A. Touat, M.M. Komnatska // Proc. of the Third World Congress in the XXI Century “Safety in Aviation and Space technology”. – Kyiv, Ukraine. – 2008. – Vol. 2, September 22−24. – P. 33.38–33.47.

Habbi A. An Improved Self- Tuning Mechanism of Fuzzy Control by Gradient Descent Method / A. Habbi, M. Zelmat // 17-th European Simulation Multiconference 9−12 June, 2003, Foundations For Successful Modelling and Simulation ESM 2003. − P. 43−48.


How to Cite

Komnatska, M. M., & Tunik, A. A. (2009). ROBUST STABILIZATION AND OPTIMIZATION OF FLIGHT CONTROL SYSTEM WITH STATE FEEDBACK AND FUZZY LOGICS. Proceedings of National Aviation University, 41(4), 33–41.