Optimal Control Problem: Necessary and Sufficient Conditions Part 2
Explore the optimal control problem in applied mathematics at Mustansiriyah University in Baghdad, Iraq. Delve into inequality constraints, dynamic programming, and the Hamilton-Jacobi-Bellman equation under the guidance of Assist. Prof. Dr. Radhi A. Zaboon.
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Department of Mathematics 2nd Course, 4th class, Applied Mathematics, 2020. Place: Mustansiriyah University, Bagdad, IRAQ. An optimal Control Problem Necessary & Sufficient Conditions Part 2 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 5/6/2025 1
Remarks Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/6/2025 2
Remarks: Inequality constraints on functions of the control and state variables The problem is to find the function ?(?) that minimize J. Adjoin the system differential equations to ? with multiplier function ?(?) For ? < 0 , ? = 0 , ?(?) is determined from For ? = 0 And Determine u t and (?), (?) is indeed for Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/6/2025 3
Dynamic Programming; the partial differential equation for optimal return function: Hamilton-Jacobi-Bellman Equation Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5/6/2025 4
Dynamic Programming; the partial differential equation for optimal return function: Hamilton-Jacobi-Bellman Equation Consider the general control problem. For an arbitrary initial point (?,?) . The performance index is The Optimal return function is given symbolically by The Terminal Boundary Conditions The system of equations Terminal Boundary Conditions Assist. Prof. Dr. Radhi Ali Zaboon, E_Mail: radhi_maths@yahoo.com 5
