Variational Synthesis of Controlled Dynamic Mappings

TL;DR

This paper introduces a variational approach for synthesizing controlled dynamic mappings in Hamiltonian systems, utilizing a controlling-function method that simplifies the canonization process and reduces redundancy in coordinate transformations.

Contribution

It develops a novel controlling-function method for canonical-map synthesis, improving efficiency and reducing redundancy compared to existing procedures.

Findings

The method effectively constructs controlled mappings for Hamiltonian systems.

It simplifies the canonization process with reduced computational redundancy.

The approach offers a systematic way to achieve goal-seeking synthesis in dynamic systems.

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 xpanded 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 rocedure that chooses regulated coordinate transformations as a base for a goal-seeking synthesis scheme.