Applied Mathematics - Calculus of Variations

Code 9.2.3167.8
Semester 8th
Flow M - Mathematics
Category Obligatory by selection
Credits 4
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.