Mathematical model of joint optimization of programmed and perturbed motions in discrete systems

А new mathematical model for the optimization of discrete systems is constructed in the article. The program motion and the ensemble (beam) of perturbed motions are investigated. In this case, the authors consider the joint optimization of smooth and non-smooth functionals defined on the program and perturbed motions. The variation of the functional and the necessary optimality conditions are provided. The developed mathematical technique allows solving non-standard control and optimization problems in various fields of science and technology