Problem 2. (Rendezvous Problem) Consider three cars moving on the same lane, whose initial locations at time t = 0 are ri (0), 12(0), 23(0) C R, respectively. Suppose the goal is for all three cars to meet at the same location (it does not matter where this meet-up location is). To achieve this goal, the following distributed controller can be designed: i (t) = 12(t) - :1(t) (la) 12(1) - FI(t) + 13(t) - 12(t) 2 (1b) i3(t) = 12(t) - 13(t). (1c) In other words, the leading and trailing cars will both move toward the middle car instantaneously; while the middle car will move towards the center of the leading and the trailing cars. (a) For this control strategy, analyze if as t - co, the goal of all three cars meeting at the same location (i.c. rendezvous) will be met. (b) If so, where will they eventually meet, based on their initial positions? (c) What is the dominate exponential rate at which rendezvous will be achieved as t - co? If there are several such rates, choose the one resulting in the slowest exponential decay