Real-time Hybrid System Identification with Online Deterministic Annealing

--We introduce a real-time identification method for discrete-time state-dependent switching systems in both the input-output and state-space domains. In particular, we design a system of adaptive algorithms running in two timescales; a stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale and estimates the mode-switching signal, and an recursive identification algorithm runs at a faster timescale and updates the parameters of the local models based on the estimate of the switching signal. We first focus on piece-wise affine systems and discuss identifiability conditions and convergence properties based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for switched systems, the proposed approach gradually estimates the number of modes and is appropriate for real-time system identification using sequential data acquisition. The progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off. Finally, we address specific challenges that arise in the application of the proposed methodology in identification of more general switching systems. Simulation results validate the efficacy of the proposed methodology. Hybrid systems, described by interacting continuous and discrete dynamics, are a powerful modeling tool in the analysis of systems where logic and continuous processes are interlaced, as in most complex cyber-physical systems. In addition to being able to describe switching dynamics, hybrid systems can be used as a tool to approximate highly non-linear dynamics by a collection of simpler models, and boost model explainability and robustness, by decomposing the behavior of a complex system into sub-systems where first principles and domain knowledge can be used for precise model tuning [1], [2]. As a result, hybrid systems have attracted significant attention in the control community. However, first principles modelling is often too complicated and sub-optimal, and a hybrid model needs to be identified on the basis of observations. The majority of the work in this area is based on piece-wise affine (PW A) systems, a class of state-dependent switched systems with important applications in identification, verification, and control synthesis of hybrid and nonlinear systems [2]-[5]. The input-output representation of PW A systems is the class of piece-wise affine auto-regressive exogenous (PW ARX) systems with the switching signal depending on a partitioning of the domain of a vector containing the recent history of input-output pairs.