Subspace identification of MIMO LPV systems using a piecewise constant scheduling sequence with hard/soft switching

A novel subspace based identification algorithm is presented which is able to reconstruct the deterministic part of a multi variable state-space Linear Parameter Varying (LPV) system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling (or weights) constant on a number of intervals. This assumption implies that the algorithm is also valid for the identification of Piece Wise Linear (PWL) systems with hard and soft switching. The intervals where the scheduling is constant allows to use LTI subspace identification methods to identify a number of models with a constant weight, stationary sequence models, with no common basis in the state space. Using the data of the transition between the stationary weight models, the crucial step can be made to relate these bases of state space to the same basis. The stationary sequence models, in the same basis, can be uniquely transferred to an LPV model. Once the LPV model is identified it is valid for other scheduling sequences as well. The sensitivity with respect to process and output noise is investigated using a Monte-Carlo simulation.