A Hierarchical Approach for the Synthesis of Stabilizing Controllers for Hybrid Systems

We consider a discretization based approach to controller synthesis of hybrid systems that allows to handle non-linear dynamics. In such an approach, states are grouped together in a finite index partition at the price of a non-deterministic over approximation of the transition relation. The main contribution of this work is a technique to reduce the state explosion generated by the discretization: exploiting structural properties of ODE systems, we propose a hierarchical approach to the synthesis problem by solving it first for sub problems and using the results for state space reduction in the full problem. A secondary contribution concerns combined safety and liveness control objectives that approximate stabilization.