Question: For the optimal control problem min J = (x2 + u2 )dt subject to r(t) +(t) = u(t) and x(0) = 4, i(0) = 0,

For the optimal control problem min J = (x2 + u2

For the optimal control problem min J = (x2 + u2 )dt subject to r(t) +(t) = u(t) and x(0) = 4, i(0) = 0, use the calculus of variations to find an ordinary differential equation whose solution yields the optimal trajectory. Note that your cost function, when written in terms of just the state, should have the form of the previous

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