Seminar Details
2012-12-11 (14.00) : On Reachability Analysis of Infinite-Dimensional Semilinear Systems
At Euler building
Organized by Mathematical Engineering
Speaker :
Elarbi Achhab (Université Cadi Ayyad and UCL)
Abstract :
Many scientific and engineering problems can be modeled by partial differential equations that can be described as differential equations in infinite-dimensional spaces, using semigroups. An interesting example is given by the dynamics of (bio) chemical tubular reactors. In contrast to finite-dimensional linear systems, many different types of controllability and reachability may be defined for these control systems. The main ones are exact controllability, approximate controllability and regional controllability on a finite time interval [0, T], for which various equivalent conditions have been obtained in the literature. In the case of semilinear control systems, the study of reachability problems require some complicated and limited assumptions. The talk presents some results in this direction under assumptions which have a simple form and can be checked in many examples. The approach is developed using a state space systems framework and is based on the use of fixed-point theorems. The main idea is to transform the reachability problem into a fixed-point problem for an appropriate nonlinear operator in a function space. This will be illustrated by a significant example.