Non commutativity and impulsive control systems


Monica Motta


Praia de Botafogo, 190, sala 317


25 de Agosto de 2016 às 16:30h

We start with a brief introduction to (non linear) impulsive control systems, which show up in several applications, to mechanics, aerospace engineering, economics. In particular, we consider a control system of the form

\dot{x}(t) = g_0(x, u, v) + \sum_{i=1}^m g_i(x, u) \dot{u}_ i     (1)

depending both on a bounded control v and on a control u, which we call impulsive, appearing in the system also with its derivative. We describe a notion of generalized (possibly discontinuous) solution for discontinuous controls u, known in the literature as graph completion solution. Following this approach, one approximates u by a sequence of smooth control functions u_k, and studies the limits of the corresponding trajectories x_k of (1). When the vector fields g_i verify a commutativity condition, these limits coincide and it is thus appropriate to define such limit function as generalized solution. In general, however, the limit depends on the choice of the approximating sequence u_k and the definition of a generalized solution becomes more involved. We concentrate on this last situation, where several results are known for controls u with bounded variation, and present some new results in the case of inputs u with unbounded variation.

*Texto informado pelo autor. 


Monica Motta received her Degree in Mathematics in 1989 and her PhD in Mathematical Physics in 1995, at Padua University. From 1995 until 1998 she was University Researcher in Mathematical Physics. Since 1998 she is Associate Professor in Mathematical Analysis at the Department of Mathematics of Padua University. Since 1998 she teaches in the branch of Padua University in Vicenza various courses of Mathematical Analysis. She authored more than thirty papers, most published on high level mathematical international journals. Her current main research topics are deterministic and stochastic optimal control theory, Hamilton-Jacobi and Isaacs-Bellman partial differential equations.