Reduction of Optimal Control Systems"
arXiv.org, 29 pages, pdf, PostScript, etc)
English translation of Chapter 1 of the
dissertation with updated references.
The paper presents necessary and sufficient
conditions for the order reduction of optimal
control systems. Exploring the corresponding
Hamiltonian system allows to solve the order
reduction problem in terms of dynamical
systems, observability and invariant
differential forms. The approach is
applicable to non-degenerate optimal control
systems with smooth integral cost function.
The cost function is defined on the
trajectories of a smooth dynamical control
system with unconstrained controls and fixed
boundary conditions. Such systems form a
category of Lagrangian systems with morphisms
defined as mappings preserving extremality of
the trajectories. Order reduction is defined
as a factorization in the category of