Models and Optimality Conditions for Hybrid Controlled Systems

摘要

On the basis of an abstract model of a time-discrete controlled system, a class of models is constructed that is convenient for describing and studying hybrid (discrete-continuous) systems. These models possess hierarchical structure with discrete controls at the upper level and continuous controls at the lower level. Families of continuous and discrete functionals of Krotov's type are introduced, in terms of which a generalized Lagrangian is constructed and sufficient optimality conditions are formulated. Then, they are concretized as the generalized Bellman scheme and used for constructing an iterative improvement algorithm of the gradient type. Applications demonstrating the efficiency of the approach are considered.