West Asia Mathematical Schools

 

 

 

 19th – 29th Dec.,  2018

Entitled:

Control and Optimization with Industrial Applications

 

 

Date and place of the school 

Date:  19-29 October  2018

Place: Department of mathematics, College of Sciences, Salahaddin University-Erbil, Erbil, Kurdistan-Iraq.

 

sponsored by

 

 

     

 

 

 

 

 

 

Please note that the certificate or/and support letter will be provided only for the participants who will attend more than 80% of the workshop sessions. 

Coordinators

• Abdeljalil Nachaoui, Laboratoire de Mathématiques-Jean Leray, Universit de Nantes, France

E-mail : [email protected]

• Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala.

 E-mail : [email protected]

 

Lecturers

• Abdeljalil Nachaoui, Laboratoire de Mathematiques Jean Leray, University of Nantes, France (   ). 
• Jaroslaw Wozniak, University of Szczecin, Szczecin, Poland, ([email protected]).
• Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala, Iraq ( ) .
• Radhi Ali Zaboon, Department of mathematics, College of Sciences, University of AlMostansriya, Iraq ([email protected]  ) .
• Mourad Nachaoui, Department of Mathematics, University of Sultan Moulay Sliman Beni Mellal, Morocco ( [email protected])

Scientific committee

• Abdeljalil Nachaoui, Laboratoire de Mathe?matiques Jean Leray, University de Nantes, France ( ).
• Jaroslaw Wosniak, University of Szczecin, Szczecin, Poland, ([email protected]).
• Tamaz Tadumdaze (Institute of Applied Mathematics, Tbilisi State University, Tbilisi,Georgia),

 

 

 

Local Organizing committee

Director: Dr Herish Omer, College of Sciences, department of Mathematics, Salahaddin University-Erbil ([email protected])  

                                                                

Co-chair : Dr Rostam Karim Saeed, College of Sciences, department of Mathematics, Salahaddin University-Erbil  ([email protected]).

Member : Dr Wuria Xoshnaw, Head of the Mathematics Department, College of Science, Salahaddin University-Erbil ([email protected]).

Member : Karzan Ahmed, College of Sciences, Department of Mathematics, Salahaddin University-Erbil ( [email protected]).

Member: Saman Ahmed Bapir, Mathematics Department, College of Science, Salahaddin University-Erbil ([email protected]).

Member: Ms Evar Lutfalla Sadraddin, Mathematics Department, College of Science, Salahaddin University-Erbil ([email protected] ). 

 

Member: Mahammed AM Rassheed, Mathematics Department, College of Science, Karkuk University ([email protected]).

 

Description of Schools

Abstract: Optimal control is concerned with control laws that maximize a specified measure of a dynamical system’s performance. This course is a rigorous introduction to the classical theory of optimal control. The topics covered in this course include optimization, the calculus of variations, Pontryagin’s principle, dynamic programming, linear quadratic optimal control, delay differential equation, shape optimisation.

Optimal control problems are generally nonlinear and therefore, generally do not have analytic solutions (e.g., like the linear-quadratic optimal control problem). As a result, it is necessary to employ numerical methods to solve optimal control problems. We describe techniques used to approach these classes of problems

 

    

Description of Course

 

1. Introduction. o Motivation : examples from industry o Optimisation : state of the art 2. A review of analysis o Basic function spaces o Definitions Properties of Hilbert space of Hilbert spaces Integration by parts in dimension d and applications Distributions 1. Review of Mathematical Programming o Convex Analysis, o Constrained and Unconstrained Problems, o Line search methods, Lagrange multipliers o Dynamic programming: principle of optimality, dynamic programming, discrete LQR 2. Hamilton-Jacobi-Bellman equation: o differential pressure in continuous time, HJB equation, Continuous LQR 3. Calculus of Variations and Optimal Control o Basic CoV Problem, o Euler-Lagrange Equations, CoV and Optimal Control, Numerical Methods Maximum Principle o Statement of MP, o Proof of MP, Bang-bang Control Classical control theory: o Controllability, o Observability Stability 1. Semigroups of operators 2. Controllability of infinite dimensional systems: Moment problem method 3. Stability of infinite dimensional systems: Transfer function method 4. Delay Differential Equation and its Comparison with ODE Numerical methods 5. Mathematical models and Delay optimal control o Development of the optimal control theory for functional differential equations o Model of the flying apparatus o Model of the economical growth 6. Delay optimal control problems with non-fixed initial moment o Problem with discontinuous initial condition and its effect. o Linear time-optimal control problem o Inverse problems Problems with the continuous initial condition and its effect Problems with the mixed initial condition (general case) and its effect Shape optimisation as part of the optimal control theory o Definition o Examples Techniques: Iterative methods using shape gradients, Genetic Algorithms