Consider the following optimal control problem: Min J = (-2x+3u+u)dt s.t. x=x+u x(0)=5 0u(t) 2 (a) Use maximum principle to solve for the optimal control, find the Hamiltonian function H(,x,u). (b) Find the costate path - i(t) and the costate final condition (2). (c) From part (b), find (t), where 0 t 2. (Hint: the general solution to the differential equation x(t) = ax(t) + b is x(t) = Ceat - b/a, where C is an arbitrary constant) [2 points] (d) Find the optimal control u*(t) analytically.