PhyThematics 20 — Pontryagin’s maximum principle
In optimal control theory, Pontryagin’s maximum principle is used to determine the optimal control strategy for transitioning a dynamical system between states, particularly when input or state controls are constrained. It says that any optimum control plus the optimal state trajectory are required to solve the two-point boundary value issue known as the “Hamiltonian system,” plus a maximum condition of the control Hamiltonian. Under specific convexity criteria on the goal and constraint functions, these required conditions become sufficient [1].
REFERENCES:
[1] https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_principle
[2] For those interested in diving deeper into the intricacies of optimal control problems, I highly recommend an in-depth course offered by MIT through their OpenCourseWare. This course, titled ‘Principles of Optimal Control (Spring 2008),’ covers a comprehensive range of topics from the foundational theories to practical applications in control systems. You can explore the full syllabus and course materials here: MIT’s Principles of Optimal Control. It’s an invaluable resource for anyone looking to expand their knowledge and expertise in this fascinating area of study.
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Originally published at http://science2be.wordpress.com on April 12, 2024.
