Wednesday, September 13, 2017
Speaker: Miriam García Soto
Venue: IST Austria
The central problem addressed in this talk is the following: given the design of a hybrid system, conclude if the system is stable. Hybrid systems are apt to model cyber-physical systems since they capture the mixed discrete-continuous behaviour which appears naturally in cyber-physical systems. Stability is a fundamental property in control system design, which demands that small perturbations in the input to the system lead to small variations in the future behaviour. The classical approach to establishing stability involves finding a particular kind of function, called Lyapunov function. In relation to this method, there is some effort towards automation which consists of a template-based search that uses sum-of-squares solvers. However, the shortcomings with this template-based method are that the choice of a correct template requires designer’s ingenuity and that a template failure does not provide instability reasons or guidance for the choice of the next template.
We propose an alternate algorithmic approach for the stability verification of hybrid systems, which is a counterexample-guided abstraction refinement (CEGAR) framework. The key idea is that given a hybrid system, its stability can be determined by constructing an abstract weighted graph which over-approximates the behaviour of the former one. The relation between the abstraction and the hybrid system is such that if every cycle in the graph has weight below 1, then the hybrid system is stable. In the case that the graph has a cycle with weight greater than 1, this cycle can be evaluated to infer instability of the hybrid system or guide the choice of subsequent templates. This CEGAR approach addresses the shortcomings of the template-based search.
We have implemented the CEGAR algorithm in the tool AVERIST, and we report experimental evaluations on some examples for demonstrating the feasibility of the approach.