Consider the bang-bang control problem of minimizing subject to the dynamics dx dt = 3 J(u) = [[5x(t) — 2u(t)]dt - 2x (t) + u(t), x(0) = 5; 0≤u(t) ≤ 1. Write down the Hamiltonian for this problem. Determine the switching times. Determine the optimal control u* (t) and state x*(t).

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