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Exercise for Optimal control – Week 1 Choose two problems to solve. Exercise 1 (Fundamental lemma of CoV). Let f be a real valued function defined on open interval (a, b) and f satisfies ∫ b a f(x)h(x)dx = 0 for all h ∈ Cc(a, b), i.e., h is continuous on (a, b) and its support, i.e., the closure of {x : h(x) ̸= 0} is contained in (a, b). 1) Show that f is identically zero if f is continuous. If f
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex1.pdf - 2025-07-08