CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS AND NONLINEARITY

A control system is a dynamical system on which one can act by using ``controls'. A control system is controllable if, for every pair of states, one can steer the control system from the first state to the second one. We survey in this talk some methods to check if a control system is controllable, specially if the control is modelled by partial differential equations and in the case where the nonlinearity plays a crucial role. Applications are presented to control systems in fluid dynamics.