Online optimization of the time scale in adaptive Laguerre-based filters

Abstract

Abstract-A new online method to optimize the free parameter in adaptive Laguerre-based filters is presented. It is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error. The proposed technique presents a fast convergence and a good robustness.

Optimal expansions of discrete-time Volterra models using Laguerre functions

“…In the work cited above, the authors showed that problem (8) has an analytic strict global solution if the corresponding linear model is BIBO stable ( ∞ k1=0 |h 1 (k 1 )| ¡ ∞) and strictly proper (h 1 (0)=0). This solution has been shown to globally minimize the upper bound of the squared norm of the error resulting from the truncation of the Laguerre series into a ÿnite number of functions (Tanguy et al, 1995(Tanguy et al, , 2000. In the sequel, these results are extended to the optimal expansion of Volterra models of any order.…”

“…Later, Fu and Dumont (1993) approached this problem in the context of linear discrete-time systems by deriving an analytic optimal solution which forces a fast convergence of the function series by linearly increasing the cost assigned to each additional Laguerre coe cient. Tanguy, Vilbà e, and Calvez (1995) and Tanguy, Morvan, Vilbà e, and Calvez (2000) showed that this analytic solution minimizes the upper bound of the squared norm of the error resulting from the truncation of the series into a ÿnite number of functions. In the context of non-linear systems, Campello, Amaral, and Favier (2001) generalized Fu and Dumont's approach to second-order Volterra models by proposing the use of two independent Laguerre bases for the expansion of the ÿrst-and second-order Volterra kernels.…”

Unique condition for generalized Laguerre functions to solve pole position problem

“…: Finding the derivative of both sides of (1) with respect to γ and, after that, simplifying this expression leads to (6). □…”

“…In fact, this analytical solution has a major drawback concerned with the necessity for finding the roots of high-order polynomials, which can entail an enormous computational cost. This point, as a consequence, led to a substantial number of studies [2][3][4][5][6][7][8][9][10] into implicit, but improved methods to avoid the mentioned disadvantage. However, Clowes's explicit solution is still of considerable interest in signal processing applications.…”

Model Predictive Control for Block-oriented Nonlinear Systems with Input Constraints

“…Proof :F o ra n yµ > 1, one has (45)- (48) governed by the control law (49), (53) and (58), if Assumption A1 and the following assumption A2 hold, then S and S e defined respectively by (56) and (57) are invariant sets and the control law (53) satisfies (48). Assumption A2) there exist σ > 0, µ 1 > 1, µ 2 > 1 and positive definite and symmetric matrices P, P e ,suchthat…”