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A TIME-FUEL OPTIMAL CONTROL PROBLEM OF A CRUISE MISSILE BASED ON AN IMPROVED SLIDING MODE VARIABLE STRUCTURE MODEL

Part of: Control systems Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  02 June 2010

R. LI  and
Y. J. SHI
R. LI*
Affiliation:
School of Automation, University of Electronic Science and Technology of China, Chengdu 611731, PR China (email: hitlirui@gmail.com)
Y. J. SHI
Affiliation:
Institute of Astronautics & Aeronautics, University of Electronic Science and Technology of China, Chengdu 611731, PR China (email: Yingjing.Shi@gmail.com)
*
✉For correspondence; e-mail: hitlirui@gmail.com
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Abstract

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The inadequacy of the traditional sliding mode variable structure (SMVS) control method for cruise missiles is addressed. An improved SMVS control method is developed, in which the reaching mode segment of the SMVS control is decomposed into an acceleration accessing segment, a speed keeping segment, and a deceleration buffer segment. A time-fuel optimal control problem is formulated as an optimal control problem involving a switched system with unknown switching times and subject to a continuous state inequality constraint. The new design method is developed based on a control parametrization, a time scaling transform and the constraint transcription method. A sequence of approximate optimal parameter selection problems is obtained with fixed switching time points and a canonical state inequality constraint. Each approximate optimal parameter selection problem can be solved effectively by using existing gradient-based optimization techniques. The convergence of these approximate optimal solutions to the true optimal solution is assured. Simulation results show that the proposed method is highly effective. The response speed of the missile under the control law obtained by the proposed method is improved significantly, while the elevator of the missile is constrained to operate within its permitted range.

Keywords

cruise missileoptimal control theorycontrol parametrizationtime scaling transformsliding mode variable structure control

MSC classification

Secondary: 49N90: Applications of optimal control and differential games 93C95: Applications
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 2 , October 2009 , pp. 261 - 276
Copyright
Copyright © Australian Mathematical Society 2010

References

[1] Boeing, “U.S. Air Force demonstrates precision-strike accuracy in CALCM”, Aerospace and Defense Industry News, St Charles, Missouri, 2001,http://www.boeing.com/news/releases/2001/q2/news_release_010508n.htm.Google Scholar
[2]Cummings, M. L., “The double-edged sword of secrecy in military weapon development”, Technol. Soc. Mag., IEEE 22 (2003) 4–12.CrossRefGoogle Scholar
[3]Farhadinia, B., Teo, K. L. and Loxton, R. C., “A computational method for a class of non-standard time optimal control problems involving multiple time horizons”, Math. Comput. Modelling 49 (2009) 682–691.CrossRefGoogle Scholar
[4]Gao, Y., Gu, L. X. and Pan, L., “Application of variable structure control in missile electromechanical actuator system” in: International Conference on Intelligent Computation Technology and Automation, China, 2008, 313–316.CrossRefGoogle Scholar
[5] “RGM/UGM-109BIC ‘tomahawk”’, Jane’s Naval Weapons Systems (Jane’s Information Group, 2001).Google Scholar
[6]Hicks, S., “Advanced cruise missile guidance system description”, IEEE National Aerospace and Electronics Conference, USA, 1993, 355–361.Google Scholar
[7]Hu, Y. N., Geng, B. L. and Li, J., “Control technique research on vertically launched missiles based on variable structure control”, in: Control and Decision Conference, China, 2008, 2866–2871.CrossRefGoogle Scholar
[8]Lechevin, N. and Rabbath, C. A., “Backstepping guidance for missiles modeled as uncertain time-varying first-order systems”, in: American Control Conference, China, 2007, 4582–4587.CrossRefGoogle Scholar
[9]Lopez, R. G., “An expert systems approach for automating performance analysis of the air launch cruise missile tests”, in: Cost Effective Support into the Next Century, Conference Proceedings, 1994, 515–525.Google Scholar
[10]Loxton, R. C., Teo, K. L. and Rehbock, V., “Computational method for a class of switched system optimal control problems”, IEEE Trans. Automat. Control 54 (2009) 2455–2461.CrossRefGoogle Scholar
[11]Loxton, R. C., Teo, K. L., Rehbock, V. and Ling, W. K., “Optimal switching instants for a switched capacitor dc/dc power converter”, Automatica 45 (2009) 973–980.CrossRefGoogle Scholar
[12]Loxton, R. C., Teo, K. L., Rehbock, V. and Yiu, K. F. C., “Optimal control problems with a continuous inequality constraint on the state and control”, Automatica 45 (2009) 2250–2257.CrossRefGoogle Scholar
[13]Ma, H. Z., Ma, G. F. and Shi, Y. J., “Study of variable structure control law for cruise vehicle with large-space variable trajectory”, J. Astronaut. 30 (2009) 199–204.Google Scholar
[14]Shi, Y. J. and Ma, G. F., “On the inversion of the Laplace transform for resolvent families in UMD spaces”, Aust. N. Z. Ind. Appl. Math. J. 49 (2008) 573–587.Google Scholar
[15]Shi, Y. J., Ma, G. F. and Ma, H. Z., “The robust stability analysis for a cruise missile”, J. Syst. Eng. Electron. 19 (2008) 785–790.Google Scholar
[16]Teo, K. L., Goh, C. J. and Wong, K. H., A unified computational approach to optimal control problems, 1st edn (Longman, New York, 1991).Google Scholar
[17]Teo, K. L., Jennings, L. S., Lee, H. W.  J. and Rehbock, V., “The control parameterization enhancing transform for constrained optimal control problem”, J. Aust. Math. Soc. Ser. B 40 (1999) 314–335.CrossRefGoogle Scholar
[18]Wang, L. Y., Gui, W. H., Teo, K. L., Loxton, R. C. and Yang, C. H., “Time-delayed optimal control problems with multiple characteristic time points: computation and industrial applications”, J. Ind. Manag. Optim. 5 (2009) 705–718.CrossRefGoogle Scholar
[19]Wu, C. Z. and Teo, K. L., “Global impulsive optimal control computation”, J. Ind. Manag. Optim. 2 (2006) 435–450.CrossRefGoogle Scholar
[20]Wu, T. B., Yin, H. and Huang, X. L., “A fuzzy logic based approach to compensating for the dynamic inverse error in the cruise missile TF/TA system”, in: 27th Chinese Control Conference, China, 2008, 420–424.Google Scholar
[21]Xu, J. T., Cui, N., Tian, J. C. and Liu, H. L., “Study on dynamic decoupling design by using ina method for cruise missile”, in: Systems and Control in Aerospace and Astronautics, 2nd International Symposium, France, 2008, 1–5.CrossRefGoogle Scholar
[22]Yeh, F. K., Cheng, K. Y. and Fu, L. C., “Variable structure based nonlinear missile guidance and autopilot design for a direct hit with thrust vector control”, in: The 41st IEEE Conference on Decision and Control, China, 2002, 1275–1280.Google Scholar