Optimal Control Problem: Necessary & Sufficient Conditions
Explore the optimal control problem with equality constraints and delve into the necessary and sufficient conditions for finding local minimums. Learn from Dr. Radhi A. Zaboon, Assistant Professor at Al-Mustansiriyah University, as he provides insights and examples on scalar quantity optimization. Discover the key principles for determining stationary points and ensuring positive definiteness in mathematical matrices.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Department of Mathematics 2nd Course, 4th class, Applied Mathematics, 2020. Place: Mustansiriyah University, Bagdad, IRAQ. An optimal Control Problem (Introduction-2) Necessary & Sufficient Conditions By Dr. Radhi A. Zaboon Assist. Prof. Department of Mathematics College of Science, Al_Mustansiriyah University Baghdad, IRAQ. E_Mail: r.zaboon@uomustansiriyah.edu.iq radhizaboon@gmail.com Radhi_maths@yahoo.com Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 1
Problem with equality constraints: The sufficient conditions Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 2
If one place ?? = ?, one can write for ??; note ??= ? If the nominal point is a stationary point; ??= 0 & ??? ?? = 0; one have the following Thus, the sufficient conditions for a local minimum are the necessary conditions and the positive definiteness (semi-definite) of the above Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 matrix 3
Example 2: The Necessary & Sufficient Conditions Example 2: Find the scalar quantity that minimizes the following constrained problem The Objective Function The Constraint Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 4
The solution The Necessary Conditions for a stationary point : The Sufficient Conditions: Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 5
Thanks Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/27/2025 6
