🤖 AI Summary
This paper addresses real-time identification of discrete-time state-dependent switching systems. We propose a two-time-scale adaptive algorithm: on the slow time scale, an online deterministic annealing mechanism estimates the unknown mode-switching signal and progressively identifies the number of modes; on the fast time scale, recursive least squares updates parameters of local models. To our knowledge, this is the first work to incorporate deterministic annealing into online switching system identification, thereby eliminating the need for prior knowledge of the number of modes—a key limitation of conventional methods—while ensuring both identifiability and computational efficiency. Theoretical analysis, grounded in stochastic approximation theory, accommodates both input–output and state-space modeling frameworks and supports piecewise-affine structures. Simulation results demonstrate the algorithm’s convergence, robustness, and low-latency adaptability, achieving high modeling accuracy while significantly improving real-time efficiency.
📝 Abstract
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.