Mathematical modeling of the human walking on the basis of optimization of controlled processes in biodynamical systems

Journal article, 2001

We propose a new statement of the problem of optimal control over a nonlinear dynamical system with phase restrictions concerning the mathematical modeling of human walking. We develop an algorithm for obtaining an approximate solution of the formulated problem of optimal control on the basis of the parametrization of independently varied functions by cubic smoothing splines and on the basis of the minimization of the objective function in orthogonal directions. The efficiency of the algorithm is illustrated by the numerical simulation of human walking at a normal pace along a horizontal surface.