Numerical Implementation of the Contact of Optimal Trajectory with Singular Regime in the Optimal Control Problem with Quadratic Criteria and Scalar Control
Previous works by these authors offer the numerical methodof successive approximations for developing the solutionsof the problemof stabilization of nonlinear systems with standard functional. This paperconsiders applying this method for studying the problem with singularcontrol. It is achieved by introducing an auxiliary problem. The solutionfor the auxiliary problem provides smooth approximation tothe solutionof the initial problem. The paper presents the algorithms for constructingan approximate solution for the initial problem. It is demonstrated that,unlike direct algorithms of optimal control, these algorithms allow toregister the saturation point, thus enabling one to register and studysingular regimes.