An Alternative Approach to Switching Hyperplane Estimation in PWA Systems

Usually the identification of piecewise affine systems consists of two steps. First, subsystem parameters are identified before the state space partition is reconstructed. For the later step, it is common to label the states of a recorded trajectory and separate differently labeled states with the help of linear support vector machines. In this paper, we present an alternative approach to estimate switching hyperplanes in continuous time piecewise affine systems. The presented approach builds upon three components. First, a hybrid observer reconstructs the switching signal up to a bounded delay. Second, we remove the delay in the reconstructed switching signal by solving an optimization problem. We obtain more precise switching states that lie on a specific switching hyperplane. Third, the switching hyperplanes are fitted to the switching states with Total Least Squares. The paper illustrates the presented approach on a numerical example.