Iterative control synthesis algorithm in a singular perturbed nonlinear problem based on the SDRE technology

The paper presents an iterative method for solving the stabilization problem for one class of nonlinear dynamical systems with “fast” and “slow” motions, where the systems are formally linear, but their coefficients depend on the state. The stabilizing controller is constructed on the basis of the movements separation principle and modification of the SDRE approach, which consists in using the iterative method of solving the Riccati matrix equation for a singularly perturbed optimal control problem.