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An optimal control problem involving a class of linear time-lag systems

Published online by Cambridge University Press:  17 February 2009

K. L. Teo ,
K. H. Wong  and
Z. S. Wu
K. L. Teo
Affiliation:
Department of Industrial and Systems Engineering, National University of Singapore, Kent Ridge, Singapore 0511, Republic of Singapore.
K. H. Wong
Affiliation:
Department of Appllied Mathematics, University of Witwatersrand, 1, Jan Smuts Avenue, Johannesberg 2001, South Africa.
Z. S. Wu
Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou, China.
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A class of convex optimal control problems involving linear hereditary systems with linear control constraints and nonlinear terminal constraints is considered. A result on the existence of an optimal control is proved and a necessary condition for optimality is given. An iterative algorithm is presented for solving the optimal control problem under consideration. The convergence property of the algorithm is also investigated. To test the algorithm, an example is solved.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 93 - 113
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Ahmed, N. U. and Teo, K. L., Optimal control of distributed parameter systems (North-Holland, New York, 1981).Google Scholar
[2]Banks, H. T. and Burns, J. A., “Hereditary control problems: numerical methods based on averaging approximations”, SIAM J. Control Optim. 16 (1978), 169–208.CrossRefGoogle Scholar
[3]Craven, B. D., Mathematical programming and control theory (Chapman and Hall, London, 1978).CrossRefGoogle Scholar
[4]Georganas, N. D., “Optimal control for a class of hereditary systems”, Ph.D. Thesis, University of Ottawa, Ottawa, Canada, 1970.Google Scholar
[5]Mayne, D. Q., Polak, E. and Heunis, A. J., “Solving nonlinear inequalities in a finite number of iterations”, J. Optim. Theory Appl. 33 (1981), 207–221.CrossRefGoogle Scholar
[6]Polak, E., Computational methods in optimization (Academic Press, New York, 1971).Google Scholar
[7]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 (5) (1977), 741–751.CrossRefGoogle Scholar
[8]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), 291–313.CrossRefGoogle Scholar
[9]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
[10]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
[11]Teo, K. L. and Wu, Z. S., Computational methods for optimizing distributed systems (Academic Press, Orlando, 1984).Google Scholar
[12]Wong, K. H. and Teo, K. L., “A conditional gradient method for a class of time-lag optimal control problems”, J. Austral. Math. Soc. Ser. B 25 (1984), 518–537.CrossRefGoogle Scholar
[13]Wu, Z. S. and Teo, K. L., “A computational algorithm for a distributed optimal control problem of parabolic type with terminal inequality constraints”, J. Optim. Theory Appl. 43 (1984), 457–476.CrossRefGoogle Scholar