Algorithms of Optimal Control Methods for Nonlinear Systems with Constraints

The contribution presents defined problems of a control of nonlinear systems, processes with constraints and limitations. Optimality conditions for a control and iterative gradient methods of nonlinear systems optimization have been given. The defined problem with the Lagrangian criterion function is converted to an optimalization problem of the theory of games. In order to solve such a problem, the search for a saddle point of a functional, an algorithm of an iterative method has been designed. There are also presented algorithms designed based on gradient methods (e.g. Generalized Method of Reduced Gradient) using the projection principles to solve mathematical models of the tasks of processes optimal control, where constraining conditions and limitations to state and control variables of the process are fulfilled.