Rigorous solution vs. fast update: Acceptable computational delay in NMPC

2011 ◽  
Author(s):  
Inga J. Wolf ◽  
Lynn Wurth ◽  
Wolfgang Marquardt
Keyword(s):  
Rigorous Solution

SOLVING THE INVERSE PROBLEM FOR FUNCTION/IMAGE APPROXIMATION USING ITERATED FUNCTION SYSTEMS I: THEORETICAL BASIS

Fractals ◽  
1994 ◽  
Vol 02 (03) ◽  
pp. 325-334 ◽  
Author(s):  
BRUNO FORTE ◽  
EDWARD R. VRSCAY
Keyword(s):  
Inverse Problem ◽  
Function Approximation ◽  
Image Representation ◽  
Iterated Function Systems ◽  
Rigorous Solution ◽  
Compact Metric Space ◽  
Image Approximation ◽  
Iterated Function ◽  
Contractive Operator ◽  
Contraction Maps

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over ℒp (X, µ): An N-map IFS with grey level maps (IFSM), to be denoted as (w, Φ), is a set w of N contraction maps wi: X → X over a compact metric space (X, d) (the "base space") with an associated set Φ of maps ϕi: R → R. Associated with each IFSM is a contractive operator T with fixed point [Formula: see text]. We provide a rigorous solution to the following inverse problem: Given a target υ ∈ ℒp(X, µ) and an ∊ > 0, find an IFSM whose attractor satisfies [Formula: see text].

Differential Quadrature Element Method for the Analysis of Vibration of Frame Structures Having Nonprismatic Members Considering Warping Torsion

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Vibration Analysis ◽  
Differential Quadrature ◽  
Frame Structures ◽  
Rigorous Solution ◽  
Discrete Eigenvalue ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Domain Boundaries ◽  
Eigenvalue System ◽  
Element Method

Abstract The differential quadrature element method (DQEM) and the extended differential quadrature (EDQ) have been proposed by the author. The EDQ is used to the DQEM vibration analysis frame structures. The element can be a nonprismatic beam considering the warping due to torsion. The EDQ technique is used to discretize the element-based differential eigenvalue equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall discrete eigenvalue system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall discrete eigenvalue system. Mathematical formulations for the EDQ-based DQEM vibration analysis of nonprismatic structures considering the effect of warping torsion are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained.

Truss Analyses by DQEM

1999 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Algebraic Equation ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Equation System ◽  
Numerical Approach ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Rigorous Solution ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method

Abstract A new numerical approach for solving generic three-dimensional truss problems having nonprismatic members is developed. This approach employs the differential quadrature (DQ) technique to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on the domain boundary. A global algebraic equation system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the global algebraic equation system. Mathematical formulations for two-dimensional differential quadrature element method (DQEM) truss model are carried out. By using this DQEM model, accurate results of two-dimensional truss problems can efficiently be obtained. Numerical results demonstrate this DQEM model.

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