MathProblemsBank

4.26 Variational calculus

Problem: Solve the optimal control problem: \[ \begin{array}{l} \int_{0}^{1}\left(x^{2}+u^{2}\right) d t \rightarrow \text { extr }, \quad \dot{x}=x+u, \\ x(1)=1 . \end{array} \]