Asymptotic Expansions of Singularly Perturbed Quasi-Linear Optimal Systems
- 1 May 1975
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control
- Vol. 13 (3) , 572-592
- https://doi.org/10.1137/0313033
Abstract
A class of two-point boundary value problems (TPBVP’s) which arise in fixed final time free endpoint optimal control problems is considered. An asymptotic power series solution of the TPBVP is constructed with respect to a parameter whose perturbation changes the differential order of the problem. Based on a stability hypothesis, the proof of asymptotic correctness is accomplished through a successive approximation scheme.Keywords
This publication has 12 references indexed in Scilit:
- Existence and dependence on a parameter of solutions of a nonlinear two point boundary value problemJournal of Differential Equations, 1973
- The Singularly Perturbed Linear State Regulator ProblemSIAM Journal on Control, 1972
- Properties of solutions of ordinary differential equations with small parametersCommunications on Pure and Applied Mathematics, 1971
- Topics in singular perturbationsAdvances in Mathematics, 1968
- Singular perturbation method for reducing the model order in optimal control designIEEE Transactions on Automatic Control, 1968
- Two-Point Boundary Value Problems of Linear Hamiltonian SystemsSIAM Journal on Applied Mathematics, 1967
- Sufficient Conditions for the Optimal Control of Nonlinear SystemsSIAM Journal on Control, 1966
- On the conjugate point condition for the control problemInternational Journal of Engineering Science, 1965
- Singular perturbations of a boundary value problem for a nonlinear system of differential equationsDuke Mathematical Journal, 1962
- Singular perturbations of nonlinear systems of differential equations related to conditional stabilityDuke Mathematical Journal, 1956