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4 Lecture 4. Misc topics on MP and the proof of the MP In the previous lecture, we studied the maximum principle. The main result is the following theorem. Theorem 1. Consider the system ẋ = f(x, u) with cost function J(u) = φ(x(tf )) + ∫ tf 0 L(x, u)dt and boundary constraint x(tf ) ∈ M ⊆ Rn Assume f , φ and L are C1 in x. Let (x∗(·), u∗(·)) correspond to the optimal solution to the minimiza- ti
https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lecture4.pdf - 2025-12-21
