A Computational Approach to Bisimulation of Hybrid Dynamical Systems
This work addresses the problem of symbolic model reduction for hybrid systems, which is important for verification and control, but the results are demonstrated only on a single example without quantitative comparisons.
The paper proposes an algorithm to find a minimal finite-state bisimulation for hybrid dynamical systems with discrete inputs affecting jumps, without requiring stability or time discretization. The algorithm yields the minimal bisimulation when a parameter is properly tuned.
The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The considered class of HDS allows for discrete-valued inputs that only affect the jumps (events) of the HDS. Representation of the HDS in the form of a transition system is revisited in comparison with prior works. An algorithm is proposed for solving the problem which gives the bisimulation with the minimum number of states if it already exists and also a parameter of the algorithm is properly tuned. There is no need for stability assumptions and no time discretization is applied. The results are applied to an example