Max-min control problems for constrained discrete time systems

We consider control synthesis problems for constrained discrete time nonlinear systems subject to uncertainty. The uncertainty affects the system in a form of a bounded, but known, persistent disturbance and leads, consequently, to the max-min control synthesis problems. A computational characterization of the max-min controllable sets is derived for a general nonlinear case. The max-min time optimal control of constrained piecewise affine discrete time systems is also discussed. Corresponding computational details are outlined and some illustrative examples are provided.