An approximate abstraction approach to safety control of differentially flat systems

Control for safety specifications of large nonlinear systems is a challenging task. By reducing the system to a discrete abstraction the computational demands of the controller can be greatly reduced. We propose a supervisor for differentially flat systems, based on an approximate abstraction of the flat output. By defining the abstraction on the flat output space, we simplify the design of the abstraction and further reduce the computational complexity of the resulting supervisor, and by exploiting approximate simulation techniques we obtain a controller that is simpler and more flexible than previously proposed solutions. The resulting algorithm is tested on an eight-dimensional nonlinear planar crane model.