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A computational method for free time optimal control problems, with application to maximizing the range of an aircraft-like projectile

Published online by Cambridge University Press:  17 February 2009

K. L. Teo ,
G. Jepps ,
E. J. Moore  and
S. Hayes
K. L. Teo
Affiliation:
Department of Industrial and Systems Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Singapore.
G. Jepps
Affiliation:
Weapons Systems Research Laboratory, Defence Science and Technology Organisation, Department of Defence, GPO Box 2151, Adelaide, South Australia 5001, Australia.
E. J. Moore
Affiliation:
Department of Applied Mathematics, University of New South Wales, P. O. Box 1, Kensington, N. S. W. 2033, Australia.
S. Hayes
Affiliation:
Department of Applied Mathematics, University of New South Wales, P. O. Box 1, Kensington, N. S. W. 2033, Australia.
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Abstract

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A class of non-standard optimal control problems is considered. The non-standard feature of these optimal control problems is that they are of neither fixed final time nor of fixed final state. A method of solution is devised which employs a computational algorithm based on control parametrization techniques. The method is applied to the problem of maximizing the range of an aircraft-like gliding projectile with angle of attack control.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 3 , January 1987 , pp. 393 - 413
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Balston, W., Mathematical Methods for Digital Computers (Wiley, 1960) 110–120.Google Scholar
[2]Bosarge, W. E. Jr, and Johnson, O. G., “Direct Method Approximation to the State Regulator Control Problem Using a Ritz-Trefftz Suboptimal Control”, IEEE Trans. Automat. Control AC-15 (1970), 627–631.CrossRefGoogle Scholar
[3]Elsgolc, L. E., Calculus of Variations (Pergamon Press, London, 1962).Google Scholar
[4]Fletcher, R., “A General Quadratic Programming Algorithm”, J. Inst. Math. Applic. 7 (1971), 76–91.CrossRefGoogle Scholar
[5]Hausdorff, L., Gradient Optimization and Nonlinear Control (Wiley, New York, 1976).Google Scholar
[6]Hicks, G. A. and Ray, W. H., “Approximation Methods for Optimal Control Synthesis”, Canad. J. Chem. Eng. 49 (1971), 522–528.CrossRefGoogle Scholar
[7]Polak, E., Computational Methods in Optimization (Academic Press, New York, 1971).Google Scholar
[8]Polak, E. and Mayne, D. Q., “A Feasible Directions Algorithm for Optimal Control Problems with Control and Terminal Inequality Constraints”, IEEE Trans. Automat. Control AC-22 (1977), 741–751.CrossRefGoogle Scholar
[9]Sirisena, H. R., “Computation of Optimal Controls Using a Piecewise Polynomial Parametrization”, IEEE Trans. Automat. Control AC-18, (1973), 409–411.CrossRefGoogle Scholar
[10]Siresena, H. R. and Chou, F. S., “Computation of Constrained Optimal Controls Using Parametrization Techniques”, IEEE Trans. Automat. Control AC-19 (1974), 431–433.CrossRefGoogle Scholar
[11]Teo, K. L. and Moore, E. J., “On Directional Derivatives Methods for Solving Optimal Parameter Section Problems”, Internat. J. Systems Sci. 9 (1978), 1029–1041.CrossRefGoogle Scholar
[12]Teo, K. L. and Moore, E. J., “Computational Methods for a Class of Time Delayed Optimal Control Problems”, Nanta Mathematica 12 (1979), 203–221.Google Scholar
[13]Teo, K. L., Wong, K. H., and Clements, D. J., “Optimal Control Computation for Linear Time-Lag Systems with Linear Terminal Constraints”, J. Optim. Theory Appl. 44 (1984), 509–526.CrossRefGoogle Scholar
[14]Teo, K. L., Wong, K. H., and Clements, D. J., “A Feasible Directions Algorithm for Time-Lag Optimal Control Problems with Control and Terminal Inequality Constraints”, J. Optim. Theory Appl. 46 (1985), 295–317.CrossRefGoogle Scholar
[15]Teo, K. L. and Womersley, R. S., “A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Terminal Inequality Constraints”, Numer. Funct. Anal. Optim. 6 (1983), 297–313.CrossRefGoogle Scholar
[16]Teo, K. L. and Wu, Z. S., Computational Methods for Optimizing Distributed Parameter Systems (Academic Press, Orlando, 1984).Google Scholar
[17]Wong, K. H. and Teo, K. L., “A Conditional Method for a Class of Time-Lag Optimal Control Problems”, J. Austral. Math. Soc. Ser. B 25 (1984), 518–537.CrossRefGoogle Scholar
[18]Wong, K. H., Teo, K. L. and Clements, D. J., “Optimal Control Computation for Nonlinear Time-Lag Systems”, J. Optim. Theory Appl. 47 (1985), 91–107.CrossRefGoogle Scholar