Hybrid tracking with impacts

Reference paper for this page:

Follow the bouncing ball: global results on tracking and state estimation with impacts.

F. Forni, A. Teel, L. Zaccarian. IEEE Transactions on Automatic Control, 58(6), 1470-1485.

Goal: tracking of the read ball r. the linear control law u=k(x-r) up to time 20. The hybrid control law u= k(x-m(q,r)) replaces the linear one from time 20. m(q,r) selects the current reference to track: for q = 0, the reference is the upper red ball (identity); for q=1, the reference is the "mirrored" lower red ball (see the blue circle). The logic variable changes its value at each impact.

Same goal as above but for a ball moving on a billiard. Left cartoon: the linear control law u=k(x-r) drives the white ball. Right cartoon, the hybrid control law u= k(x-m(q,r)) drives the white ball. m(q,r) selects the current reference to track: for q = 0, the reference is the centered red ball. For different values of q, the reference is one of the "mirrored" red balls. The green rectangle indicates the current selected reference. The logic variable changes its value at each impact, in accordance with a 9 states automaton, reported in the paper.