State-Space Piece-Wise Affine System Identification with Online Deterministic Annealing

We propose an online identification scheme for discrete-time piece-wise affine state-space models based on a system of adaptive algorithms running in two timescales. A stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale, estimating the partition of the augmented state-input space that defines the switching signal. At the same time, an adaptive identification algorithm, running at a higher timescale, updates the parameters of the local models based on the estimate of the switching signal. Identifiability conditions for the switched system are discussed and convergence results are given based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for piece-wise affine systems, the proposed approach progressively estimates the number of modes needed and is appropriate for online system identification using sequential data acquisition. This progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off, desired in practical applications. Experimental results validate the efficacy of the proposed methodology.