On Modification of the Positional Optimization Method for a Class of Nonlinear Systems

Abstract

An optimal control problem in a class of nonlinear systems is considered. A modification of the positional optimization approach to the optimal control of feedback type synthesis is suggested. The problem of nonlinear control is reduced to a problem of optimal control for an auxiliary linear approximation system at each step of algorithm, and then to a linear programming problem. If the time to solve the auxiliary linear problem does not exceed the algorithm time step, we can say that the control system realizes the positional control in real time. The proposed method is illustrated with an optimal control problem for the mathematical pendulum.