I module: (12 hours)
INTRODUCTION TO THE OPTIMAL CONTROL
Some introductory problems The problem of lunar landing, the foundation of Carthage and the extraction of a finite resource, a production problem and consumption, the construction of roads in the mountains.
II module (12 hours):
Formulation of an optimal control problem Definition of controls, dynamic, trajectories, together with the control. Controls eligible and within regions. Importance of the case of linear dynamics.
III module (12 ore): The OPTIMAL CONTROL METHOD WITH VARIATIONAL The simplest problem of optimal control theorem of Pontryagin comments, and the consequences of the maximum principle. extremal control, associated multiplier. Normal and Abnormal control. Sufficient optimality conditions: the condition of Mangasarian and the condition of Arrow. conditions for problems with starting / ending points set. On minimum problems.
IV module (12 hours)
Production model and inventory management I.The simplest problem of the calculus of variations Euler's theorem; the Euler equation in special cases. conditions for problems with starting / ending points set. sufficient conditions for the simpler problem using concave / convex. minimum length curve.Controls singular and bang-bang-bang-bang of definitions controls, switching instants and unique controls. The construction of a mountain road at minimal cost. more general problem of optimal control of Mayer Problems, Bolza and Lagrange: their equivalence. A necessary condition for the final time Bolza problem with fixed or free. Bolza problems in the calculation of variations: the necessary and sufficient conditions. The adjustment model of labor demand (Hamermesh).
ITALIAN VERSION
