2. The objective of this problem is to understand a timed automaton, and then to mod- ify it as specified. (a) For the timed automaton shown below, describe the output y. Avoid imprecise or sloppy notation. continuous variables: rs ER output: y ER r(t) = 1/y:=s(t) r(t):= 0 s(0) := 0 r(0) :=0 two one s(t) = 1 $(t) = 1 r(t) = 1 r(t) = 1 r(t) = 2/y:= s(t) r(t) = 0 (b) Assume there is a new pure input reset, and that when this input is present, the hybrid system starts over, behaving as if it were starting at time 0 again. Modify the hybrid system from part (a) to do this