Methods and apparatus are described for control of friction at the nanoscale. A method of controlling frictional dynamics of a plurality of particles using non-Lipschitzian control includes determining an attribute of the plurality of particles; calculating an attribute deviation by subtracting the attribute of the plurality of particles from a target attribute; calculating a non-Lipschitzian feedback control term by raising the attribute deviation to a fractionary power .xi.=(2m+1)/(2n+1) where n=1, 2, 3 . . . and m=0, 1, 2, 3 . . . , with m strictly less than n and then multiplying by a control amplitude; and imposing the non-Lipschitzian feedback control term globally on each of the plurality of particles; imposing causes a subsequent magnitude of the attribute deviation to be reduced.
STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY-SPONSORED RESEARCH OR DEVELOPMENT
This invention was made with United States Government support under prime contract No. DE-AC05-00OR22725 to UT-Battelle, L.L.C. awarded by the Department of Energy. The Government has certain rights in this invention.