Parameter set estimation algorithms for time-varying systems

Parameter set estimation (PSE), a class of system identification schemes which aims at characterizing the uncertainty in the identification experiment, is philosophically different from traditional parameter estimation schemes which seek to identify a single point (model) in the parameter space. The literature has seen a good deal of attention paid to PSE techniques in recent years, primarily because it is projected that they will play a vital role in robust identification for control. An important step in current research along these lines is development of PSE algorithms for systems which are time varying in nature; this is particularly true if the identified model set is to be used in an adaptive setting, such as for gain scheduling or autotuning. In this paper, we extend an ellipsoid algorithm for PSE of time-invariant systems to time-varying systems. We show how knowledge of dependences in the parameter variations can be exploited to reduce the number of computations in the resulting algorithm. Finally, scalar bound inflation, a second strategy for PSE of time-varying systems, is optimized for volume, and a comparison of the two algorithms is made.