Technical Report No. UniTS-DI3.2001.1 Robust Minimum-time Constrained Control of Nonlinear Discrete-Time Systems: New Results

This work is concerned with the analysis and the design of robust minimum-time control laws for nonlinear discrete-time systems with possibly non robustly controllable target sets. We will show that, given a Lipschitz nonlinear transition map with bounded control inputs, the reachability properties of the target set can be used to assess the existence of a robust positively controllable set which includes the target in its interior. This result will be exploited to formulate a robustified minimum-time control scheme capable to ensure the ultimate boundedness of the trajectories in presence of bounded uncertainties even if the target set is not robust positively controllable.