Method of control local improvement for non-homogeneous discrete systems

In studying of non-homogeneous control systems by different schools the main attention is paid to continuous systems with time-varying structure. The necessary and sufficient conditions, as well as iterative procedures have been obtained for them. One of the approaches is to generalize the sufficient conditions for optimality of Krotov type on such systems. On this basis a non-homogeneous hierarchical model of controlled structure have been developed in which the lower level is a description of similar processes at different stages, and the upper level connects these descriptions into a single process, and controls the functioning of the system in whole. In various control problems, in particular in optimization problems, both levels are considered in interaction. We have considered the class of non-homogeneous discrete systems for which both levels are discrete. These systems are prevalent in practice and can be obtained from the process of continuous systems digitalization for solution of optimization problems using iterative methods. We have formulated the sufficient conditions of optimality of Krotov type for this class of systems. These conditions and the principle of localization are used to construct improvement method. The article contains illustrative examples.