Singular extremal of optimal control problems with L^1 cost
Michele Motta (SISSA, Trieste)
Jeudi 5 décembre, 14h00, salle Euler Violet.
Abstract. We consider the optimal control problem given by a control affine system, with control in a ball, where we want to minimize the L^1 norm of the control. This kind of problems arises in aerospace engineering, where this model is used to minimize the fuel consumption. The minimization of the L^1 norm appears also in many problems where the expected optimal solutions have periods of time with control equal to zero.
When applying Pontryagin Maximum Principle to this optimal control problem, one finds that there are extremals, which are called singular, whose control is not determined directly by PMP. For these extremals, we derived second order necessary conditions for optimality. Furthermore, we also found sufficient conditions that ensures strong optimality among admissible trajectory close to the singular one in the C^0 – uniform topology.
This is a joint work with A.Agrachev and I. Beschastny.