Online identification of piecewise affine systems

In this paper, we present a novel procedure for online identification of piecewise affine systems. We show how to identify the submodels of a piecewise affine system online, under the assumption of known switching boundaries and full state measurement. The adaptively identified subsystem parameters can be used for indirect adaptive control or online plant diagnosis and fault detection. The procedure proposed in this paper extends the well-studied series-parallel parameter identifiers in adaptive control to piecewise affine systems. Challenges that had to be solved for this extension are the additional constant input of the affine subsystems and the switching behavior which is a potential source of instability. We sketch the proof for both stability and parameter convergence of the proposed algorithm. Finally, numerical simulations validate the results and analyze the convergence speed of the estimated parameters.