Controllability of Infinite Dimensional Systems with Control Constraints

In this paper we examine the controllability properties of infinite dimensional control systems, nonlinear in the control variable and with time varying control constraints. We derive a necessary and sufficient condition for approximate controllability, which in the case of linear, autonomous finite dimensional control systems with no control constraints reduces to the classical Kalman rank condition. We also study the problem of approximate local null-controllability and compare the controllability properties of the original and relaxed systems.