Interpolating model identification for SISO linear parameter-varying systems

This paper presents a new method to estimate linear parameter-varying (LPV) state-space models for single-input single-output systems whose dynamics depend on one or more time-varying parameters, called scheduling parameters. The method is based on the interpolation of linear time-invariant models that are identified for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The proposed method can account for multiple scheduling parameters and yields either a polynomial or an affine LPV model that is numerically well-conditioned and therefore suitable for LPV control synthesis. The underlying interpolation technique is formulated as a nonlinear least-squares optimization problem that can be solved efficiently by standard solvers. The new interpolation method is applied to an electromechanical system that depends on two scheduling parameters. The numerical results are compared to existing techniques in the literature, demonstrating the potential and advantages of the proposed method.