Learning hybrid models with logical and continuous dynamics via multiclass linear separation

Hybrid dynamical models are a powerful tool for describing the behaviour of many industrial processes and physical phenomena in which logical (discrete) and analog (continuous) dynamics exist and interact. Black-box identification of hybrid models from input/output observations and no information on the operating mode of the system is a challenging problem, as both the logical and the continuous dynamics must be retrieved. In this work, we consider the identification of discrete hybrid automata (DHA), which represent a mathematical abstraction of hybrid models whose logical dynamics are described by a finite state machine (FSM) and the continuous dynamics are represented through affine discrete-time dynamical models. We propose a two-stage estimation algorithm based on the joint use of clustering, multi-model recursive least-squares and linear multicategory discrimination techniques, which allows us to estimate both the affine models describing the continuous dynamics and the FSM governing the logical dynamics of the system.