Applied Mathematics - Calculus of Variations
|Flow||M - Mathematics|
|Category||Obligatory by selection|
|Class Hours - Lab Hours||4 - 0|
|Lecturers||Iasson Karafyllis (School of AMPS), Ioannis Tsinias (School of AMPS)|
An introduction to the calculus of variations: necessary and sufficient conditions for extremals ; Euler-Lagrange equations. Extremals under constraints: Lagrange’s multipliers. Optimal control: Linear control systems, attainable sets; topological properties; controllability. The time-optimal control problem for linear control systems; extremal control; maximum principle. Minimization of quadratic cost for the case of linear control systems with no magnitude restraints;. Riccati equation. Nonlinear systems: topological properties of attainable sets; extremal control; Pontryagin’s Maximum Principle; necessary conditions for optimal control with and without magnitude restraints. Sufficient conditions and existence theorems. The Hamilton-Jacobi-Bellman equation. Applications.