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The parabolic spline collocation method of the solution to an optimal control problem with aftereffect. (English. Russian original) Zbl 0888.65078
Dokl. Math. 53, No. 2, 225-226 (1996); translation from Dokl. Akad. Nauk 347, No. 4, 449-450 (1996).
Summary: Systems with aftereffect are often encountered in different industrial problems, mechanical systems, etc. Many authors have considered numerical methods for solving optimization problems for such systems. In this work, we reduce an optimization problem to the investigation of a boundary value problem by G. A. Kharatishvili’s maximum principle [Dokl. Akad. Nauk SSSR 136, 39-42 (1961; MR 23#A 404)]. To solve the latter problem numerically, we develop a new collocation method based on parabolic splines. We derive an existence and convergence theorem for approximations.
65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M15 Newton-type methods