The first step in using the Hamilton-Jacobi-Bellman equation 0 = J*(x(t), t) + min {g(x(t), u(t), t) +JT(x(1), t)[a(x(1), u(t), t)]} a (t) is to determine the admissible control u*(?) [in terms of x(t), t, and J*] that minimizes { }. Find u*(t)-expressed as a function of x(t), t, and J-for the system (1) = x2(1) っ() = -x,() + x,() + u), and the performance measure J = [q1x}(t) + 92x3(1) + u*(1)] dt, 91, 92 > 0. The admissible controls are constrained by |u(t)|S1.

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