A Direct Multiple Shooting Method for Missile Trajectory Optimization with The Terminal Bunt Manoeuvre

S. Subchan Subchan

Abstract


Numerical solution of constrained nonlinear optimal control problem is an important field in a wide range of applications in science and engineering. The real time solution for an optimal control problem is a challenge issue especially the state constrained handling. Missile trajectory shaping with terminal bunt manoeuvre with state constaints is addressed. The problem can be stated as an optimal control problem in which an objective function is minimised satisfying a series of constraints on the trajectory which includes state and control constraints. Numerical solution based on a direct multiple shooting is proposed. As an example the method has been implemented to a design of optimal trajectory for a missile where the missile must struck the target by vertical dive. The qualitative analysis and physical interpretation of the numerical solutions are given.

Keywords


terminal bunt manoeuvre; missile trajectory; direct multiple shooting

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References


H. J. Kelley, Methods of gradients In Optimization Techniques with Application to Aerospace systems (ed. G. Leitmann), vol. 5,Mathematics in Science and Engineering Academic press, New York, 1962, pp. 206–254.

A. E. Bryson and W. F. Denham, “A steepest ascent method for solving optimum programming problems,” ASME Journal of Applied Mechanics Series E,” pp. 247–257, 1962.

R. Pytlak, Numerical Methods for Optimal Control Problems with State Constraints vol. 1707 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, Berlin, 1999.

C. R. Hargraves and S. W. Paris, “Direct trajectory optimization using nonlinear programming and collocation”, Journal Guidance, Control, and Dynamics, vol. 10, no. 4, 1987, pp. 338–342.

E. D. Dickmanns and K. H. W ll, “Approximate solution of optimal control problems using third order Hermite polynomial functions,” in Proceedings of the IFIP Technical Conference, Springer-Verlag, 1974, pp. 158–166.

R. R. Kumar and H. Seywald. Fuel-optimal station keeping via differential inclusion. Journal of Guidance, Control, and Dynamics, vol. 18, no. 5, pp. 1156–1162, 1995.

H. Seywald. “Trajectory optimization based on differential inclusion,” Journal of Guidance, Control, and Dynamics, vol. 17, no, 3, pp. 480–487, 1994.

H. B. Keller. Numerical Methods for Two-Point Boundary Value Problems. Dover Publications, New York, 1992.

J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Springer, New York, 3rd ed, 2002.

U. M. Ascher, R. M. M. Mattheij, and R. D. Russel. Numerical Solution of Boundary Value Problem for Ordinary Differential Equations. SIAM, Philadelphia, 1995.

P. E. Gill, W. Murray, and M. H. Wright. “SNOPT: An SQP algorithm for large scal constrain d optimization,” SIAM Journal on Optimization, vol. 12, no. 4, 2002, pp. 979–1006.

S. Subchan and . Żbiko ski. “Computational optimal control of the terminal bunt manoeuvre - Part 1: Minimum altitude case, “Optimal Control Applications & Methods, vol. 28, no. 5, 2007, pp. 311–353.

S. Subchan and R. Żbiko ski, Computational optimal control: tools and practices, John Wiley and Sons, Chichester, 2009.




DOI: http://dx.doi.org/10.12962/j20882033.v22i3.67

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