Section: New Results

Extending robustness and randomization from consensus to symmetrization algorithms

Participant : Alain Sarlette.

In the framework of a collaboration with Francesco Ticozzi (University of Padova) on common points between quantum and classical network dynamics, we developed a general "symmetrization" framework which covers robust ways to generate dynamics in several algorithmic and control contexts [18] . The starting point was the question of generalizing so-called "consensus" algorithms to networks composed of quantum units. In order to define state information exchange without requiring state communication (an impossible feat given the quantum no-cloning theorem), an operational viewpoint on consensus had been proposed by Alain Sarlette and co-authors in the previous year. In this new result, the scope of this operational viewpoint is considerably extended by considering it as a "symmetrization" procedure with respect to some discrete group, completely abstracting away the actual action space. It is shown that this abstraction covers existing procedures ranging from network synchronization to random state generation (not in networks) and averaging-based open-loop control procedures. The interest of viewing those procedures under the common "symmetrization" framework proposed is twofold: convergence proofs follow from a general result that we have established; and robustness to randomized actions and (specific) parameter uncertainties is shown to carry over from the "consensus" literature. It is further anticipated that the approach might be a guideline for new algorithmic designs in the future.