Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-29T15:20:00.081Z Has data issue: false hasContentIssue false

Nonlinearly constrained optimal control problems

Published online by Cambridge University Press:  17 February 2009

K. L. Teo
Affiliation:
Dept. of Mathematics, University of Western Australia, Nedlands, W.A., Australia.
K. H. Wong
Affiliation:
Dept. of Applied Mathematics, Univesity of the Witwatersrand, Johannesburg, South Africa.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Bosarge, W. E. Jr. and Johnson, O. G., “Direct method approximation to the state regulator control problem using at Ritz-Trefftz suboptimal control,” IEEE Trans. Auto. Control Vol. AC-15 (1970) 627631.CrossRefGoogle Scholar
[2] Bryson, A. E. Jr. and Ho, Y. C., Applied optimal control, (Halsted Press, New York, 1969).Google Scholar
[3] Cesari, L., Optimization: theory and applications, (Springer-Verlag, New York, 1983.)CrossRefGoogle Scholar
[4] Goh, C. J. and Teo, K. L., “Control parametrization: a unified approach t to optimal control problems with general constraints,” Automatica 24 (1988) 318.CrossRefGoogle Scholar
[5] Gonzalez, S. and Miele, A., “Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions,” JOTA 26 (1978) 395425.CrossRefGoogle Scholar
[6] Hasdorff, L., Gradient optimization and nonlinear control, (John Wiley, 1976).Google Scholar
[7] Hicks, G. A. and Ray, W. H., “Approximation methods for optimal control systems,” Can. J. Chem. Eng. 49 (1971) 522528.CrossRefGoogle Scholar
[8] Jennings, L. S., Fisher, M. E., Teo, K. L. and Goh, C. J., MISER3: Optimal control software, theory and user manual, EMCOSS, Perth, 1990.Google Scholar
[9] Miele, A., “Recent advances in gradient algorithms for optimal control problems,” JOTA 17 (1975) 361430.CrossRefGoogle Scholar
[10] Miele, A. and Wang, T., “Primal-dual properties of sequential gradient-restoration algorithms for optimal control problems, Part 1, Basic Problems,” in Payne, F. R. et al., (ed.), Integral Methods in Science and Engineering, (Hemisphere Publishing Corporation, Washington, DC, 1986) 577607.Google Scholar
[11] Miele, A. and Wang, T., “Primal-dual properties of sequential gradient-restoration algorithms for optimal control problems, Part 2, general problem,” J. Math. Anal. Appl. 119 (1986) 2154.CrossRefGoogle Scholar
[12] Sakawa, Y. and Shindo, Y., “Optimal control of container cranes,” Automatica 18 (1982) 257266.CrossRefGoogle Scholar
[13] Schittkowski, K., “NLPQL: a FORTRAN subroutine solving constrained nonlinear programming problems,” Operations Research Annals 5 (1985) 485500.CrossRefGoogle Scholar
[14] Sirisena, H. R., “Computation of optimal controls using a piecewise polynomial parametrization,” IEEE Transl. Auto. Control AC-18 (1973) 409411.CrossRefGoogle Scholar
[15] Sirisena, H. R. and Chou, F. S., “An efficient algorithm for solving optimal control problems with linear terminal constraints,” IEEE Trans. Auto. Control Vol. AC-21 (1976) 275277.CrossRefGoogle Scholar
[15] Sirisena, H. R. and Chou, F. S., “Convergence of control parameterization Ritz method for nonlinear optimal control problems,” JOTA 19 (1979) 369382.CrossRefGoogle Scholar
[17] Sirisena, H. R. and Tan, K. S., “Computation of constrained optimal controls using parametrization techniques,” IEEE Trans. Auto. Control AC-19 (1974) 431433.CrossRefGoogle Scholar
[18] Teo, K. L. and Goh, C. J., “A computational method for combined optimal parameter selection and optimal control problems with general constraints,” J. Math. Soc. Aust. Ser. B. 30 (1989) 350364.CrossRefGoogle Scholar
[19] Teo, K. L. and Jennings, L. S., “Nonlinear optimal control problems with continuous state inequality constraints,” JOTA 63 (1989) 122.CrossRefGoogle Scholar
[20] Teo, K. L., Wong, W. H. and Clements, D. J., “Optimal control computation for linear time-lag systems with linear terminal constraints,” JOTA 44 (1984) 509526.CrossRefGoogle Scholar
[21] Wong, K. H., Clements, D. J. and Teo, K. L., “Optimal control computation for nonlinear time-lag systems,” JOTA 47 (1985) 91107.CrossRefGoogle Scholar