Robust identification of piecewise affine systems from noisy data

In this paper, we focus on the identification of discrete-time piecewise affine (PWA) systems from noisy data. This problem consists of the estimation of both the local affine subsystems and the partition of the regression space. A two-stage robust identification approach is proposed to estimate the local affine subsystems in the presence of noise. This approach includes an optimization-based initial estimation process and a least-squares-based refinement procedure. In addition, to estimate the partition of the regression space for continuous dynamic PWA systems, an intersection approach is proposed as an alternative to the widely used pattern recognition approaches. Simulation studies demonstrate the effectiveness of the two-stage identification approach and the intersection approach in noisy case.