Abstract
A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Teo, K. L., andJennings, L. S.,Nonlinear Optimal Control Problems with Continuous State Inequality Constraints, Journal of Optimization Theory and Applications, Vol. 63, pp. 1–22, 1989.
Gonzalez, S., andMiele, A.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems with General Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 26, pp. 395–425, 1978.
Miele, A., andWang, T.,Primal—Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 1: Basic Problems, Integral Methods in Science and Engineering., Edited by F. R. Payne et al., Hemisphere Publishing Corporation, Washington, DC, pp. 577–607, 1986.
Miele, A., andWang, T.,Primal—Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 2: General Problem, Journal of Mathematical Analysis and Applications, Vol. 119, pp. 21–54, 1986.
Goh, C. J., andTeo, K. L.,Control Parametrization: A Unified Approach to Optimal Control Problems with General Constraints, Automatica, Vol. 24, pp. 3–18, 1988.
Teo, K. L., andGoh, C. J.,A Computational Method for Combined Optimal Parameter Selection and Optimal Control Problems with General Constraints, Journal of the Australian Mathematical Society, Series B, Vol. 30, pp. 350–364, 1989.
Teo, K. L., andGoh, C. J.,A Simple Computational Procedure for Optimization Problems with Functional Inequality Constraints, IEEE Transactions on Automatic Control, Vol. 32, pp. 940–941, 1987.
Wong, K. H., Clements, D. J., andTeo, K. L.,Optimal Control Computation for Nonlinear Time-Lag Systems, Journal of Optimization Theory and Applications, Vol. 47, pp. 91–107, 1985.
Sirisena, H. R.,Computation of Optimal Controls Using a Piecewise Polynomial Parametrization, IEEE Transactions on Automatic Control, Vol. 18, pp. 409–411, 1973.
Sirisena, H. R., andChou, F. S.,Convergence of Control Parametrization Ritz Method for Nonlinear Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 29, pp. 369–382, 1979.
Sirisena, H. R., andTan, K. S.,Computation of Constrained Optimal Controls Using Parametrization Techniques, IEEE Transactions on Automatic Control, Vol. 19, pp. 431–433, 1974.
Teo, K. L., andWomersley, R. S.,A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Terminal Inequality Constraints, Numerical Functional Analysis and Optimization, Vol. 6, pp. 291–313, 1983.
Teo, K. L., Wong, K. H., andClements, D. J.,Optimal Control Computation for Linear Time-Lag Systems with Linear Terminal Constraints, Journal of Optimization Theory and Applications, Vol. 44, pp. 509–529, 1984.
Schittkowski, K.,NLPQL: A Fortran Subroutine Solving Constrained Nonlinear Programming Problem, Operations Research Annals, Vol. 5, pp. 485–500, 1985.
Royden, H. L.,Real Analysis, 2nd Edition, Mamillan Company, New York, New York, 1968.
Author information
Authors and Affiliations
Additional information
Communicated by M. Corless
Rights and permissions
About this article
Cite this article
Kaji, K., Wong, K.H. Nonlinearly constrained time-delayed optimal control problems. J Optim Theory Appl 82, 295–313 (1994). https://doi.org/10.1007/BF02191855
Issue Date:
DOI: https://doi.org/10.1007/BF02191855