Lee, A. Y. Hereditary optimal control problems: Numerical method based upon a Padé approximation. (English) Zbl 0617.49013 J. Optimization Theory Appl. 56, No. 1, 157-173 (1988). We consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argument x(t-\(\tau)\). In our approximation scheme, we first replace the variable with an augmented state \(y(t)\underline\triangle x(t-\tau)\). The two-sided Laplace transform of y(t) is a product of the Laplace transform of x(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation for y(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four example problems are solved to illustrate the validity and usefulness of this technique. Cited in 4 Documents MSC: 90C52 Methods of reduced gradient type 34K35 Control problems for functional-differential equations 41A21 Padé approximation 44A10 Laplace transform 65K10 Numerical optimization and variational techniques 93B40 Computational methods in systems theory (MSC2010) 93C10 Nonlinear systems in control theory Keywords:hereditary optimal control; time-delayed argument; two-sided Laplace transform; first-order Padé approximation; gradient algorithm PDF BibTeX XML Cite \textit{A. Y. Lee}, J. Optim. Theory Appl. 56, No. 1, 157--173 (1988; Zbl 0617.49013) Full Text: DOI References: [1] 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. · Zbl 0379.49025 · doi:10.1137/0316013 [2] Pol, V. B., andBremmer, H.,Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge University Press, London, England, 1955. [3] Lee, A. Y.,Optimal Landing of a Helicopter in Autorotation, Department of Aeronautics and Astronautics, Stanford University, Stanford, California, 1985. · Zbl 0850.93673 [4] Miele, A., Damoulakis, J. N., Cloutier, J. R., andTietze, J. L.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Journal of Optimization Theory and Applications, Vol. 13, pp. 218-255, 1974. · Zbl 0268.49042 · doi:10.1007/BF00935541 [5] Banks, H. T.,Approximation of Nonlinear Differential Equation Control Systems, Journal of Optimization Theory and Applications, Vol. 29, pp. 383-408, 1979. · Zbl 0387.49040 · doi:10.1007/BF00933142 [6] 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. · Zbl 0535.49029 · doi:10.1007/BF00935465 [7] 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. · Zbl 0548.49014 · doi:10.1007/BF00941318 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.