Automatic Synthesis of Robust Numerical Controllers

A major problem of numerical controllers is their robustness, i.e. the state read from the plant may not be in the controller table, although it may be close to some states in the table. For continuous systems, this problem is typically handled by interpolation techniques. Unfortunately, when the plant contains both continuous and discrete variables, the interpolation approach does not work well. To cope with this kind of systems, we propose a general methodology that exploits explicit model checking in an innovative way to automatically synthesize a (time-) optimal numerical controller from a plant specification and apply an optimized strengthening algorithm only on the most significant states, in order to reach an acceptable robustness degree. We implemented all the algorithms within our CGMur\varphi tool, an extension of the well-known CMur\varphi verifier, and tested the effectiveness of our approach by applying it to the well-known truck and trailer obstacles avoidance problem.