In this paper,we propose a united weighted Landaus type inequality for classical orthogonal polynomials Q_n(x),Q_n(x) can be Hermite function H_n(x),generalized Laguerre function L~((s))_n(x)(s>-1),or Jacobi function P~((α,β))_n(x)(α,β>-1).
In the algorithm,Laguerre functions are used to describe the control signals from the dynamic linear section of Wiener model,and the optimization solutions of the future control input sequences in predictive control are converted into the optimization of a set of immemorial Laguerre coefficients within prediction horizon in order to reduce the computation burden in optimization.
In this paper, a new predictive control scheme for Wiener type nonlinear systems based on Laguerre functions model and RBF neural networks model is presented. The combined model has advantages of both Laguerre functions model and RBF neural networks model, and has a good control for the system with changes in time delay, order and structure of nonlinear system.
针对 Wiener型非线性系统 ,本文提出了一种基于 L aguerre函数模型与 RBF神经网络模型的组合模型的预测控制策略 ,研究结果表明该组合模型兼具两者的优点 ,适用范围广 ,对系统变时延 ,变阶次及变非线性都具有良好的控制效果
The results of applying the adaptive predictive control strategy based on Laguerre model to a diffusion furnace are reported in this paper, and the principle and algorithm of the strategy are briefly introduced.
The Laguerre function and the radial Coulomb wave function are defined by their recursion relations.
An addition theorem for the Laguerre function is re-derived using these techniques.
The characteristics of the principal modes and the multi-input threshold device can be derived from Laguerre function expansions of the computed first- and second-order Volterra kernels when the system is stimulated with a randomly varying input.
The new function is a generalization of the q-Laguerre function and the Stieltjes-Wigert function.
Finally, limq→1Anα((1 - q)x, -β, 1;q) gives Ln(α,β)(x,q), which is a β-modification of the ordinary Laguerre function.
By using the properties of discrete Laguerre functions, a novel unstructured model for non-linear process is presented. And it is used to the design of generalized predictive controller for nonlinear process. An adaptive algorithm suitable for non-linear process is obtained. And a simulation example is presented to show that this algorithm is indeed effective.
In this paper, a three-term recurrence formula of discrete Laguerre functions and the definition of the unstructured model are given. The method of establishing the unstructured model of the process via discrete Laguerre functions is presented. A novel unstructured model is obtained. Based on this model, a simple generalized predictive controller is given. An example is presented to illustrate the utility of this controller.
For the two-partical Boltzmann hierarchy,we consider only such distribution functions which can be expanded in Laguerre function series.By solving the moment equations system,an equilibrium solution for two-partical Boltzmann hierarchy is obtained.It is also shown that this equilibrium solution is valid for gen- eral molecular interaction.