Parametric continuation method with correction and its applications
The main topic of this paper is to develop a reliable computationally efficient method applicable to a wide class of optimal control problems. This method, called parametric continuation method for solving nonlinear algebric and functional equations, is based on homotopy theory (fixed point homotopy, Newton homotopy etc.). Using the parametric continuation method with correction, the author propose a numerical method for solving nonlinear equations. The algorithm proposed, and the main theorem show the quality of approximation of the homotopy curve. Then, the parametric continuation method is applied to solve a nonlinear boundary-value problem for ordinary differential equations, and to find the Pontryagin extremal solution of an optimal control problem by its reduction to a boundary-value problem. Other applications are also discussed: control-nonlinear problems and affine problems with mixed constraints. Maximizer algorithms are proposed and an analytical form of the derivative is obtained.
scientific article; zbMATH DE number 5633021
scientific article