Guidance Law based on LMI-based Robust Model Predictive Control to Obtain Optimal LOS for Flying Vehicle

Authors

Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

In this paper, a new guidance law based on Robust Model Predictive Control (RMPC) is proposed for intercepting flying maneuvering targets. The presented guidance law is calculated by nonlinear kinematics. The design is based on a state feedback control law in which Linear Matrix Inequalities (LMI) has been used in order to optimize a cost function, subject to constraint on the control input. This Robust MPC method is utilized to obtain optimal Line Of Sight (LOS) angle tracking performance for maneuvering flying vehicle. It is shown that the control signal obtained from the problem stabilizes the nonlinear plant. Numerical simulations are implemented to the nonlinear plant and the effectiveness of the guidance law has been demonstrated.

Keywords


[1] C. E. Garcia, D. M. Prett and M. Morari, “Model predictive control: theory and practice-a survey,” Automatica, vol. 25, pp. 335-348, 1989.
[2] M. V. Kothare, V. Balakrishnan and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, pp.1361-1379, 1996.
[3] F. Wu, “LMI-based robust model predictive control and its application to an industrial CSTR problem,” Journal of Process control, vol.11, pp.649-659, 2001.
[4] F. A. Cuzzola, J. C. Geromel and M. Morari, “An improved approach for constrained robust model predictive control,” Automatica, vol. 38, pp. 1183-1189, 2002.
[5] L. Feng, J. Wang, E. Poh and F. Liao, “Multi-objective robust model predictive control: trajectory tracking problem through LMI formulation,” Proceedings of the American Control Conference, NY, pp. 5589-5594, July 11-13, 2007.
[6] S. D. Brierly and R. Longchamp, “Application of sliding mode control to air-air interception problem,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, pp. 306-325, 1990.
[7] R. Yanushevsky and W. Boord, “Lyapunov approach to guidance law design,” Nonlinear Analysis: Theory, Methods & Applications, vol. 63, pp. 743-749, 2005.
[8] S. H. Ding, S. H. Li and S. Luo, “Guidance law design based on continuous finite-time control technique,” Journal of Astronautics, vol. 32, pp. 727–733, 2011.
[9] S. Sefriti, J. Boumhidi, M.  Benyakhlef and I. Boumhidi, “Adaptive decentralized sliding mode neural network control of a class of nonlinear interconnected systems,” International Journal of Innovative Computing, Information and Control, vol. 9, pp. 2941–2947, 2013.
[10] M. Golestani, I. Mohammadzaman, M. J. Yazdanpanah and  A. R. Vali, “Application of finite-time integral sliding mode to guidance law design,” Journal of Dynamic Systems, Measurement, and Control, vol. 137, pp. DS-14-1113, 2015.
[11] W. Wang, S. Xiong, X. Liu, S. Wang and L. Ma, “Adaptive nonsingular terminal sliding mode guidance law against maneuvering targets with impact angle constraint,” Journal of Aerospace Engineering , vol. 229, pp. 867-890, 2015.
[12] S. He, D. Lin and J. Wang, “Continuous second-order sliding mode based impact angle guidance law,” Aerospace Science and Technology, vol. 41, pp. 199-208, 2015.
[13] S. He, W. Wang and J. Wang, “Three-dimensional impact angle guidance laws based on model predictive control and sliding mode disturbance observer,” Journal of Dynamic Systems, Measurement, and Control, vol. 138, pp. DS-15-1318, 2016.
[14] S. Shamaghdari, S. K. Y. Nikravesh and M. Haeri, “Integrated guidance and control of elastic flight vehicle based on robust MPC,” International Journal of Robust and Nonlinear Control, vol. 25, pp. 2608-2630, 2015.
[15] S. Mobayen, “An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems,” Nonlinear Dynamics, vol. 79, pp. 1075-1084, 2014.
[16] B. J. Parvat and B. M. Patre, “Fast terminal sliding mode controller design for nonlinear second-order systems with time varying uncertainties,” International Journal of Dynamics and Control, vol. 4, pp. 1-8, 2016.
[17] S. Mobayen, “An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems,” Nonlinear Dynamics, vol. 83, pp. 1557-1565, 2015.
[18] S. Mobayen, “An LMI-based robust tracker for uncertain linear systems with multiple time varying delays using optimal composite nonlinear feedback technique,” Nonlinear Dynamics, vol. 80, pp. 917-927, 2015.
[19] هاشمی، رمضانی و پارسا مقدم، «بهره‌برداری هاب انرژی با استفاده از روش کنترل پیش‌بین مبتنی بر مدل مقاوم با در نظر گرفتن خطای پیش‌بینی بار الکتریکی»، مهندسی برق دانشگاه تبریز، جلد 46، شماره 3، پائیز 95.
[20] پیروزمند، قهرمانی و عاروان، «طراحی کنترل‌کننده پیش‌بین مقاوم با استفاده از نامساوی‌های ماتریسی خطی برای سیستم کنترل وضعیت ماهواره»، مهندسی برق دانشگاه تبریز، جلد 44، شماره 4، زمستان 93