Abstract
In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.
Similar content being viewed by others
References
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. 509–526, 1984.
Sirisena, H. R., andChou, F. S.,Convergence of the Control Parameterization 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 Parameterization Techniques, IEEE Transactions on Automatic Control, Vol. AC-19, pp. 431–433, 1974.
Hicks, G. A., andRay, W. H.,Approximation Methods for Optimal Control Synthesis, Canadian Journal of Chemical Engineering, Vol. 49, pp. 522–528, 1971.
Bosarge, W. E. Jr., andJohnson, O. G.,Direct Method Approximation to the State Regulator Control Problem Using a Ritz-Trefftz Suboptimal Control, IEEE Transactions on Automatic Control, Vol. AC-15, pp. 627–631, 1970.
Sirisena, H. R.,Computation of Optimal Controls Using a Piecewise Polynomial Parameterization, IEEE Transactions on Automatic Control, Vol. AC-18, pp. 409–411, 1973.
Banks, H. T.,Approximation of Nonlinear Functional Differential Equation Control Systems, Vol. 29, pp. 383–408, 1979.
Rubinstein, Z.,A Course in Ordinary and Partial Differential Equations, Academic Press, New York, New York, 1969.
Hasdorff, L.,Gradient Optimization and Nonlinear Control, John Wiley and Sons, New York, New York, 1976.
Banks, H. T., andBurns, J. A.,Hereditary Control Problems: Numerical Methods Based on Averaging Approximations, SIAM Journal on Control and Optimization, Vol. 16, pp. 169–208, 1978.
Georganas, N. D.,Optimal Control for a Class of Hereditary Systems, University of Ottawa, PhD Thesis, 1970.
Murray, J. M., andTeo, K. L.,On a Computational Algorithm for a Class of Optimal Control Problems Involving Discrete Time Delayed Arguments, Journal of the Australian Mathematical Society, Series B, Vol. 20, pp. 315–343, 1978.
Sirisena, H. R., andChou, F. S.,State Parameterization Approach to the Solution of Optimal Control Problems, Optimal Control Applications and Methods, Vol. 2, pp. 289–298, 1981.
Sirisena, H. R., andChou, F. S.,An Efficient Algorithm for Solving Optimal Control Problems with Linear Terminal Constraints, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 275–277, 1976.
Teo, K. L., Wu, Z. S., andClements, D. J.,A Computational Method for Convex Optimal Control Problems Involving Linear Hereditary Systems, International Journal of Systems Science, Vol. 12, pp. 1045–1060, 1981.
Oguztoreli, M. N.,Time-Lag Control Systems, Academic Press, New York, New York, 1976.
Ahmed, N. U., andTeo, K. L.,Optimal Control of Distributed Parameter Systems, North-Holland, New York, New York, 1981.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Wong, K.H., Clements, D.J. & Teo, K.L. Optimal control computation for nonlinear time-lag systems. J Optim Theory Appl 47, 91–107 (1985). https://doi.org/10.1007/BF00941318
Issue Date:
DOI: https://doi.org/10.1007/BF00941318