Construction of positional solutions for optimization problems of dynamic systems in the class of continuous control bounded on amplitude and derivative

In the class of restricted controls with their restricted derivatives a linear optimal control problem for dynamic systems is under consideration. An approach to realize optimal feedback controls for a concrete process is suggested which is based on reducing the problem to a linear programming problem and consequent using the dual method of linear programming. An algorithm for Optimal controller which in real-time mode for every concrete process of functioning the system produces controls bounded on amplitudes and derivatives is justified. Results of computer experiments on realizing the optimal feedback for two mass point connected by elastic bond are given.