A method of approximating a random vector function

Cybernetics ◽  
1968 ◽  
Vol 2 (5) ◽  
pp. 58-59
Author(s):  
Ts. S. Khatiashvili
Keyword(s):  
Vector Function ◽  
Random Vector

scholarly journals Bipedal walking pattern generation and control for humanoid robot with bivariate stability margin optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401880088
Author(s):  
Liang Yang ◽  
Zhi Liu ◽  
Yong Chen
Keyword(s):  
Neural Networks ◽  
Vector Function ◽  
Random Vector ◽  
Humanoid Robot ◽  
Stability Margin ◽  
Pattern Generation ◽  
Bipedal Walking ◽  
Walking Pattern ◽  
Control Scheme ◽  
Walking Pattern Generation

This article concentrates on the problem of walking pattern generation and online control for humanoid robot. However, it is challenging and thus still remains open so far in the field of bipedal locomotion control. In this article, we solve this problem by proposing a bivariate-stability-margin-based control scheme, in which a random vector function-link neural networks mechanism is additionally contained. By utilizing opposition-based learning algorithm to generate walking patterns and designing random vector function-link neural networks for compensating the combination of zero-moment point error and modeling error, the new walking controller exhibits good performance. Moreover, a bivariate-stability-margin-based fuzzy logic system is proposed to assign a weight to each training sample according to locomotion stability. With these results, a walking control system is successfully established and experiments validate the proposed control scheme.

Dyed fabric illumination estimation with regularized random vector function link network

2020 ◽  
Author(s):  
Zhiyu Zhou ◽  
Dexin Liu ◽  
Jiushen Guo ◽  
Jianxin Zhang ◽  
Zefei Zhu ◽  
...  
Keyword(s):  
Vector Function ◽  
Random Vector ◽  
Illumination Estimation ◽  
Dyed Fabric

FAF-DRVFL: Fuzzy activation function based deep random vector functional links network for early diagnosis of Alzheimer disease

2021 ◽  
Vol 106 ◽  
pp. 107371
Author(s):  
Rahul Sharma ◽  
Tripti Goel ◽  
M. Tanveer ◽  
Shubham Dwivedi ◽  
R. Murugan
Keyword(s):  
Alzheimer Disease ◽  
Early Diagnosis ◽  
Random Vector ◽  
Activation Function

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

The Concentration Ellipsoid of a Random Vector Revisited

1991 ◽  
Vol 7 (3) ◽  
pp. 397-403 ◽  
Author(s):  
Kenneth Nordström
Keyword(s):  
Quadratic Form ◽  
Random Vector ◽  
Crucial Role ◽  
Type Inequality ◽  
Estimation Theory ◽  
Linear Estimation ◽  
Nonnegative Definite

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.

Utilization of random vector functional link integrated with manta ray foraging optimization for effluent prediction of wastewater treatment plant

2021 ◽  
Vol 298 ◽  
pp. 113520
Author(s):  
Khaled Elmaadawy ◽  
Mohamed Abd Elaziz ◽  
Ammar H. Elsheikh ◽  
Ahmed Moawad ◽  
Bingchuan Liu ◽  
...  
Keyword(s):  
Wastewater Treatment ◽  
Random Vector ◽  
Wastewater Treatment Plant ◽  
Treatment Plant ◽  
Functional Link ◽  
Manta Ray
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