Abstract: This paper proposes a nonlinear model based predictive control (NMPC) algorithm for nonlinear systems by using multiple models approach. To have a less complexity model we expand each linear sub-model on an orthogonal Laguerre basis, the characteristic pole of which should be optimized. In this paper we propose a pole optimization algorithm based on the Gauss-Newton method and we use ...

The object of this paper is to prove combinatorially several (13 of them) limit formulas relating different families of hypergeometric orthogonal polynomials in Askey’s chart classifying them. We first find a combinatorial model for Hahn polynomials which, as pointed out by Foata at the ICM (1983), “contains” models for Jacobi, Meixner, Krawtchouk, Laguerre and Charlier polynomials. Seven limit...

For a given (n − 1)-dimensional hypersurface x : M → R, consider the Laguerre form Φ, the Laguerre tensor L and the Laguerre second fundamental form B of the immersion x. In this article, we address the case when the Laguerre form of x is parallel, i.e., ∇Φ ≡ 0. We prove that ∇Φ ≡ 0 is equivalent to Φ ≡ 0, provided that either L+λB+μg = 0 for some smooth function λ and μ, or x has constant Lagu...

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. ...

A new time-domain model order reduction method based on the Laguerre function expansion of the impulse response is presented. The Laguerre coefficients of the impulse response of the reduced-order model, which is calculated using a projection whose matrices form basis of appropriate Krylov subspaces, match, up to a given order, those of the original system. In addition, it is shown that the obt...

The paper presents a model predictive control method for continuous-time systems based on subspace identification. It’s developed by reformulating the continuous-time systems using Laguerre filters to obtain the subspace prediction output. Then, the subspace predictors are derived by QR decomposition from input-output and Laguerre matrices. The subspace predictive controller is designed with th...

In this paper, ‎the multi-sensor fault diagnosis in the exhaust temperature sensors of a V94.2 heavy duty gas turbine is presented‎. ‎A Laguerre network-based fuzzy modeling approach is presented to predict the output temperature of the gas turbine for sensor fault diagnosis‎. Due to the nonlinear dynamics of the gas turbine, in these models the Laguerre filter parts are related to the linear d...

The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...

New batch and adaptive methods are proposed to optimize the Volterra kernels expansions on a set of Laguerre functions. Each kernel is expanded on an independent Laguerre basis. The expansion coefficients, also called Fourier coefficients, are estimated in the MMSE sense or by applying the gradient technique. An analytical solution to Laguerre poles optimization is provided using the knowledge ...