Identification of Piecewise Affine State-Space Models via Expectation Maximization

Abstract: This paper deals with the identification of piecewise affine state-space models. These models are obtained by partitioning the state or input domain into a finite number of regions and by considering affine submodels in each region. The proposed framework uses the Expectation Maximization (EM) algorithm to identify the parameters of the model. In most of the current literature, a discrete random variable with a discrete transition density is introduced to describe the transition between each submodel, leading to a further approximation of the dynamical system by a jump Markov model. On the contrary, we use the cumulative distribution function (CDF) to compute the probability of each submodel given the measurement at that time step. Then, given the submodel at each time step the latent state is estimated using the Kalman smoother. Subsequently, the parameters are estimated by maximizing a surrogate function for the likelihood. The performance of the proposed method is illustrated using the simulated model of the JAS 39 Gripen aircraft.