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I'm working on a homework problem in optimal controls and my plant model is described as: $$\ddot{x}(t) = u(t)$$ The performance index (cost function) is described by: $$J = 1/2\int_0^5u^{2}(t)dt\,$$ And the boundary conditions are $$x(0) = 0,$$ $$x(5)=0,$$ $$\dot{x}(0)=2$$ $$\dot{x}(5)=0$$ I'm not sure how to start this problem when I need $\dot{x}(t)$ to start with. Do I just integrate the plant model?

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