A Data-Driven Approach for Certifying Asymptotic Stability and Cost Evaluation for Hybrid Systems

In this paper, we propose a learning-based algorithm for hybrid systems with a twofold purpose: first, to design Lyapunov functions and, second, to upper bound the cost of solutions to the system. Via enforcing conditions at finitely many points of a set of interest and leveraging regularity properties of the maps defining the dynamics of the system and the stage costs associated to solutions, we extend the conditions to the entire set of interest. The method employs neural networks to learn a Lyapunov function and a value-like function to guarantee the extended pointwise conditions at all points in the set of interest and thus, guarantee practical asymptotic stability of a set or provide an upper bound on the cost of solutions, respectively. The approach is illustrated in a hybrid oscillator system.