Strong control improvement method for non-homogeneous discrete systems

The class of non-homogeneous discrete systems (NDS) with intermediate criterions is considered. These systems are two-level and are prevalent in practice. They can be also obtained via discretization of continuous systems in the process of solving optimization problems using iterative methods. For this class of systems a strong improvement method of the second order is constructed based on the analogue of Krotov type sufficient optimality conditions. The authors of the article question the assertion that for classical discrete control systems, as well as for heterogeneous ones, there is no sense in introducing the concept of a strong relative minimum. Therefore, when constructing an improvement method, we put forward the requirement of proximity of neighboring approximations from the class of admissible only by the process states at both levels. The resulting method contains a vector-matrix two-level system for conjugate variables. The increment of controls at each level linearly depends on the corresponding states, which allows finding a solution in the form of approximate linear synthesis of optimal control. The method was tested on two illustrative examples, which showed its efficiency. The application of the developed method to a more complex example allowed us to obtain a smaller value of the functional than that found earlier by a similar in structure minimax improvement method.