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# How to synchronize an out of sync system?

preprint
posted on 2021-10-03, 10:33 authored by Kahina LouadjKahina Louadj, Philippe Marthon
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.

## Email Address of Submitting Author

louadj_kahina@yahoo.fr

## ORCID of Submitting Author

https://orcid.org/0000-0002-4203-6357

IRIT-ENSEEIHT

France

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