Voronovskaya type asymptotic approximation by modified Gamma operators
Abstract In this paper we deal with the following modified Gamma operators A n ( f ; x ) = ∫ 0 ∞ K n ( x , t ) f ( t ) dt , defined for any f for which the last integral is convergent, where K n ( x , t ) = ( 2 n + 3 ) ! n ! ( n + 2 ) ! · t n · x n + 3 ( x + t ) 2 n + 4 , x , t ∈ ( 0 , ∞ ) . We study some direct results in asymptotic approximation.
Positive linear operators which preserve x2
A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione2(x) =x2 is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed.
State estimation for integrated vehicle dynamics control
This paper discusses a vehicle controller and a state estimator that was implemented and tested in a vehicle equipped with a combined braking and chassis control system to improve handling. The vehicle dynamics controller consists of a feed forward body roll compensation and a feedback stability controller. The estimator is based on a non-linear vehicle model combined with an extended Kalman filter. The Kalman filter is also connected to an algorithm, which estimates the tyre-road friction coefficient. The developed estimator was tested in a vehicle. Good results were achieved for normal and extreme driving manoeuvers.