System Identification Under General Norms for Linear Parameter Varying State-Space Systems via Sparse Matrix Methods

This paper presents a new algorithm for the globally optimal solution to the system identification problem for linear parameter varying state-space systems based on general norms, especially the p-norms. A new approach to discretizing the problem leads to a p-norm based cost function that is reduced to a function of only the system parameters and the unknown state of the system at a single time point. In the case of Gaussian measurement errors (p = 2) the cost function is reduced to a function of only the system parameters. The method takes full advantage of the sparse nature of the matrices involved in order to accelerate the optimization, and can be used over any time interval in the measurement data without prior knowledge of initial/boundary conditions. The method is tested with a synthetic time-varying system, as well as with real measurement data from a pendulum on a cart.