Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems

Transient stability assessment (TSA) helps prevent a safety-critical system from experiencing catastrophic incidents, such as a blackout for power systems. Under parametric stochasticity, the TSA process becomes very challenging in the sense that it must be performed multiple times as the system doesn’t remain stationary. In case the TSA isn’t repeated each time the system alters, it results in a very conservative stability region which isn’t very informative to the system operator. In this context, we propose a meta-learning-based adaptive Lyapunov function that adapts to any parametric shifts and performs a TSA on the new system. To achieve this, we integrate neural Lyapunov functions (NLFs) with model agnostic meta-learning (MAML) framework to propose meta-neural Lyapunov functions (meta-NLFs). These meta-NLFs train across a set of deterministic instances of a system under parametric stochasticity. During deployment, a fully trained meta-NLF swiftly adapts (in one gradient update) to a test-time system and correspondingly, generates a meaningful stability region. Through rigorous simulation results on different dynamical systems (two power systems and three benchmark control systems), we showcase the superiority in performance of meta-NLF over other baseline TSA methods.

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