On the Relationship Between the Enforced Convergence Criterion and the Asymptotically Optimal Laguerre Pole

When approximating dynamic systems with Laguerre basis functions (LBFs) it is important to tune the Laguerre pole such that the expansion can be both parsimonious and accurate. Expressing the sum of squared errors (SSE) as a function of the Laguerre pole leads to an objective function that has many local minima and therefore cannot be optimized directly. Two alternative methods have been proposed in the literature: an asymptotically optimal method, and the enforced convergence criterion (ECC). In this paper, a generalization of the ECC will be investigated such that in the limit minimizing this generalized ECC and computing the asymptotically optimal solution lead to the same Laguerre pole. Moreover, it will be proved that these generalized ECCs are quasiconvex functions which means they can be efficiently minimized using numerical optimization techniques. The concept of operator quasiconvexity is investigated and used to prove quasiconvexity of the ECC.