Patent ID: 7693587

Claim:
A method, comprising controlling frictional dynamics of a plurality of separate individual particles using non-Lipschitzian feedback control including: measuring a property of the plurality of separate individual particles; calculating a velocity of the plurality of separate individual particles as a function of the property, the velocity of the plurality of separate individual particles being a center of mass velocity V cm = ( 1 / N ) ⁢ ∑ n = 1 N ⁢ ⁢ ϕ . n , where N is a total number of the plurality of separate individual particles; calculating a velocity deviation by subtracting the velocity of the plurality of separate individual particles from a target velocity; calculating a non-Lipschitzian feedback control term comprising a non-Lipschitzian terminal attractor and a non-Lipschitzian terminal repeller, the terminal attractor being calculated by raising the velocity deviation to a fractionary power ξ=(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; calculating a time dependent average velocity v av that represents a moving run-time average of v cm , wherein the non-Lipschitzian feedback control term is represented by: C ( t )=α( v target −v cm ) ξ −β( v av −v cm ) ξ sgn[( v av −v cm )( v cm −v target )] H[r−|v target −v av |], wherein α is the control amplitude and represents a weight of the non-Lipschitzian terminal attractor, β is another control amplitude and represents another weight of the non-Lipschitzian terminal repeller, H(.) denotes a Heaviside function defined as H(z)=1 for z>0, H(z)=1 for z=0 and H(z)=0 for z<0, r represents a threshold, v target is the target velocity, v target −v cm is the velocity deviation; and imposing the non-Lipschitzian feedback control term globally on each of the plurality of separate individual particles, wherein imposing causes a subsequent magnitude of the velocity deviation to be reduced.