Comments on "Stochastic choice of basis functions in adaptive function approximation and the functional-link net" [with reply]

1997 ◽  
Vol 8 (2) ◽  
pp. 452-454
Author(s):  
Jin-Yan Li ◽  
W.S. Chow ◽  
B. Igelnik ◽  
Yoh-Han Pao
Keyword(s):  
Function Approximation ◽  
Basis Functions ◽  
Adaptive Function ◽  
Functional Link ◽  
Stochastic Choice

scholarly journals A New Improved Penalty Avoiding Rational Policy Making Algorithm for Keepaway with Continuous State Spaces

2009 ◽  
Vol 13 (6) ◽  
pp. 675-682 ◽  
Author(s):  
Takuji Watanabe ◽  
◽  
Kazuteru Miyazaki ◽  
Hiroaki Kobayashi ◽  
◽  
...  
Keyword(s):  
Basis Function ◽  
Function Approximation ◽  
Policy Making ◽  
Basis Functions ◽  
State Spaces ◽  
Soccer Game ◽  
Continuous State ◽  
Current Input ◽  
Multiagent Environments ◽  
Parp 1

The penalty avoiding rational policy making algorithm (PARP) [1] previously improved to save memory and cope with uncertainty, i.e., IPARP [2], requires that states be discretized in real environments with continuous state spaces, using function approximation or some other method. Especially, in PARP, a method that discretizes state using a basis functions is known [3]. Because this creates a new basis function based on the current input and its next observation, however, an unsuitable basis function may be generated in some asynchronous multiagent environments. We therefore propose a uniform basis function and range extent of the basis function is estimated before learning. We show the effectiveness of our proposal using a soccer game task called “Keepaway.”

scholarly journals Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial

2008 ◽  
Vol 5 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Function Approximation ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Least Square ◽  
Orthogonal Functions ◽  
Functional Differential ◽  
Approximated Evaluation ◽  
Chebyshev Functions

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

Position and Attitude Control of Underactuated Drones Using the Adaptive Function Approximation Technique

2020 ◽  
Author(s):  
Azin Shamshirgaran ◽  
Donald Ebeigbe ◽  
Dan Simon
Keyword(s):  
Disturbance Rejection ◽  
Function Approximation ◽  
Control Method ◽  
System Stability ◽  
Linear Feedback ◽  
Approximation Technique ◽  
Adaptive Function ◽  
Edge Tracking ◽  
Highly Nonlinear ◽  
Function Approximation Technique

Abstract Despite the popularity of drones and their relatively simple operation, the underlying control algorithms can be difficult to design due to the drones’ underactuation and highly nonlinear properties. This paper focuses on position and orientation control of drones to address challenges such as path and edge tracking, and disturbance rejection. The adaptive function approximation technique control method is used to control an underactuated and nonlinear drone. The controller utilizes reference attitude signals, that are derived from a proportional derivative (PD) linear feedback control methodology. To avoid analytic expressions for the reference attitude velocities, we employ a continuous-time Kalman filter based on a model of the measurement signal — which is derived by passing the reference attitude position through a low-pass signal differentiator — as a second-order Newtonian system. Stability of the closed loop system is proven using a Lyapunov function. Our design methodology simplifies the control process by requiring only a few tuning variables, while being robust to time-varying and time-invariant uncertainties with unknown variation bounds, and avoids the requirement for the knowledge of the dynamic equation that governs the attitude of the drone. Three different scenarios are simulated and our control method shows better accuracy than the proportional-derivative controller in terms of edge tracking and disturbance rejection.

scholarly journals Eksponencijalne atomske bazne funkcije : razvoj i primjena

2016 ◽  
Author(s):  
◽  
Nives Brajčić Kurbaša
Keyword(s):  
Exponential Type ◽  
Function Approximation ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Practical Application ◽  
Software Module ◽  
Practical Advantage ◽  
First Time ◽  
Derivatives Of ◽  
Basic Level

In this work basic properties of algebraic Atomic Basis Functions (ABF) are systematized and, using analogous approach, ABF of exponential type, so far known only at the basic level, are developed. For the first time the properties of exponential ABFs are thoroughly investigated and expressions for calculating the values and all the necessary derivatives of the functions in an arbitrary points of the domain are developed as well as some special features required for their practical application in a form suitable for numerical analysis. A software module for calculating all necessary values of the exponential ABFs, including its own graphics support, is created within this work. Thus, the exponential ABF is prepared to use as users or compiler function. The presented 1D verification examples of the function approximation and the examples of solving differential equations illustrate and confirm the practical advantage of the ABFs of the exponential type in relation to the, so far mostly used, algebraic functions, especially for describing expressed fronts and/or waves contained in the numerical solutions of various technical tasks.

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