Optimal Control Problem in Applied Mathematics at Mustansiriyah University, Baghdad
Explore an optimal control problem in applied mathematics without terminal constraints, involving a continuous system at Mustansiriyah University, Baghdad. Dr. Radhi A. Zaboon guides the process of finding the minimizing function and integrating differential equations for optimal performance. Discover the necessary conditions for optimality and two-point boundary value problems in this intriguing study.
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Department of Mathematics 2nd Course, 4th class, Applied Mathematics, 2020. Place: Mustansiriyah University, Bagdad, IRAQ. An optimal Control Problem Continuous system; No Terminal Constraints; Fixed Terminal Time 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 6/20/2025 1
The problem is to find the function ?(?) that minimize J. Adjoin the system differential equations to ? with multiplier function ?(?) Integrate the last term on the right side of ? scalar (Hamiltonian) function Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 6/20/2025 2
Condider the variation in ? due to variations in the Control vector ? ? for fixed times ????? ?? Choose the multiplier function ?(?) to cause the coefficients of ?? in ? ? to vanish, for simplicity. The boundary condition Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 6/20/2025 3
In summary, to find a control vector function ? ? that produces A stationary value of the performance index ?, we must solve the following differential equations (Euler-Lagrange) equations: Or ? ? ?? ?????????? Two-Point Boundary Value Problem And The Necessary Conditions for Optimality Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 6/20/2025 4
Remark:If ? and ? are not explicit functions of the time ? (????? ?) If u(t) is an optimal control In order that ? be local minimum, not only ?? the second order expression for ?? holding ? ? = ?, must nonnegative for all values (infinitesimal) of ?? that is one have: ??=0 but in addition, Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 6/20/2025 5
The Sufficient conditions for optimality Where Or This equation determines ??(?) in term of ??(?), but in complicated way Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 6/20/2025 6
