Variational Synthesis of Controlled Dynamic Mappings

Abstract

The article deals with the subject of solving the problem of canonical-map synthesis for Hamiltonian systems. For this purpose, the controlling-function method has been developed that allows appropriate changes of the variables in terms of calculus of canonical variation, starting from their target conditions. To use the canonical formalism, the initial dynamic system that employs changing Lagrange multipliers is reduced to a Hamiltonian system in an expanded phase space, followed by the construction of controlling function. The algorithm suggested for the canonization of controlled mappings has an advantage over the known procedures, and first of all, redundancy in the procedure that chooses regulated coordinate transformations as a base for a goal-seeking synthesis scheme.