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Application of a nonlinear stabilizer for localizing search of optimal trajectories in control problems with infinite horizon

The research is focused on an algorithm for constructing solutions of optimal control problems with infinite time horizon arising, for example, in economic growth models.    
There are several significant difficulties which complicate 
solution of the problem, such as: 
(1) stiffness of Hamiltonian systems generated by the Pontryagin maximum principle; (2) non-stability of equilibrium points; (3) lack of initial conditions for adjoint variables. 
 
The analysis of the Hamiltonian system 
implemented in this paper 
for optimal control problems with infinite horizon 
provides results effective 
for construction of optimal solutions, namely, 
(1) if a steady state exists and satisfies regularity conditions 
then there exists a nonlinear stabilizer for the Hamiltonian system; (2) a nonlinear stabilizer generates the system 
with excluding adjoint variables 
whose trajectories 
(according to qualitative analysis of the corresponding differential equations) 
approximate solutions of the original Hamiltonian system 
in a neighborhood of the steady state;(3) trajectories of the stabilized system serve 
as first approximations and localize search of optimal trajectories. 
  
The results of numerical experiments 
are presented by modeling 
of an economic growth system 
with investment in capital 
and enhancement of the labor efficiency.