How to synchronize an out of sync system?

Synchronization with other machines is one of those tasks that an
intelligent machine should be able to perform. To do so, a general
method of synchronization must be defined and that is the ambition of
this article. For this purpose, we recall what the main concepts of
systemic modelling consist of. Then we define what a Synchronization
Problem is and distinguish three types of synchronization problems :
predetermined (PSP), stochastic (SSP) and asymptotic (ASP). So, to find
the best solution, we define three optimized synchronization problems :
Optimized Predetermined Synchronization Problems , Optimized Stochastic
Synchronization Problems (OSSP) and Optimized Asymptotic Synchronization
Problems (OASP). A general method for solving an optimized
synchronization problem and thus synchronize an out of sync system, is
then given; it includes four steps : step 1, identify the
synchronization functions; step 2, identify the synchronization case :
predetermined, stochastic or asymptotic; step 3, select an optimization
criterion and solve the optimized synchronization problem corresponding
to the chosen synchronization case; step 4, find a control which permits
to track the system trajectory, optimal solution of the selected
optimized synchronization problem. In the next section, we present a
heuristic algorithm that checks the constraints of an ASP for any
initial state of the system to be synchronized. The principle of this
algorithm is to pursue or track a perfectly synchronized solution.
Finally, we present and solve two synchronization problems in the field
of Mobile Robot Systems: a synchronized satelliteization problem and the
Horse Carousel Problem. We apply to these two problems the general
method given above by choosing the asymptotic synchronization case and
our tracking algorithm. Simulation results show the efficiency of the
method and the relevance of using a tracking algorithm.