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Identification of Linear Switching System with Unknown Dimensions

Switching systems have the property that their dynamical behavior may switch between a number of different modes. Identification of switching systems consists of identifying both the individual models which describe the system in the various modes, as well as the time instants when the mode changes have occurred. This soft computing problem therefore consists of numerically demanding coupled parameter identification and clustering problem. In this contribution a method based on sparse optimization techniques is proposed for identification of switching systems. In the two proposed methods, the modes and the associated models are determined one by one by solving linear problems which are sparse with respect to the number of violated epsilon-insensitive constraints and also solving by extending the models with an alternative LP-formulation of the optimization problem. The performance of the identification procedure is demonstrated by simulated examples.