3.19 A given system is characterized by x, + x1 + x1 = m, where x1(0) = c1 and x1(0) A x2(0) = C2 are constants, x1(7) and o x1(T) = x2(T) are required to be zero, and T is the terminal time which is to be minimized subject to the constraint Im, (t)| being less than or equal to unity for all t. Prove that the optimal mi(t), m,*(t), which yields the minimum of T assumes either the value +1 or the value -1 at all but at most a finite number of instants of time in the interval [0,7]. (Hint: Use the first + method of Section 3-8d; show that the costate variables (Lagrange multipliers) corresponding to x, and X2, X2 = x1, have solutions which are nonzero, in general, at all but at most a finite number of points in [0, 7]; use this fact in conjunction with the set of Euler-Lagrange equations to obtain the proof.)