scholarly journals Damped inertial dynamics with vanishing Tikhonov regularization: Strong asymptotic convergence towards the minimum norm solution

2022 ◽  
Vol 311 ◽  
pp. 29-58
Author(s):  
Hedy Attouch ◽  
Aïcha Balhag ◽  
Zaki Chbani ◽  
Hassan Riahi
Keyword(s):  
Tikhonov Regularization ◽  
Asymptotic Convergence ◽  
Minimum Norm ◽  
Minimum Norm Solution

Failure recovery for wrench capability of wire-actuated parallel manipulators

Robotica ◽  
2011 ◽  
Vol 30 (6) ◽  
pp. 941-950 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Parallel Manipulators ◽  
Failure Recovery ◽  
Partial Recovery ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Actuator Failures ◽  
Force Moment ◽  
Hybrid Actuation

SUMMARYWire-actuated parallel manipulators and their failures are studied in this paper taking into consideration their failure modes. A methodology for investigating the effect of wire/actuator failures on the force/moment capability of manipulators is presented, and the criteria for full and partial recovery from these failures are established. The methodology is also applicable for the cases that the minimum norm solution for the vector of wire tensions gives a negative value for tension by treating the corresponding wire as failed. The proposed criteria are also valid for the manipulators that utilize hybrid actuation of wires and joints. Three planar wire-actuated parallel manipulators are used as the case study to illustrate the proposed methodology and criteria.

scholarly journals A Regularized Gradient Projection Method for the Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Yao ◽  
Shin Min Kang ◽  
Wu Jigang ◽  
Pei-Xia Yang
Keyword(s):  
Projection Method ◽  
Minimization Problem ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Gradient Projection Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Gradient Projection Algorithm

We investigate the following regularized gradient projection algorithmxn+1=Pc(I−γn(∇f+αnI))xn,n≥0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problemminx∈Cf(x).

Structural Identification Using Order Overspecified Time-Series Models

1992 ◽  
Vol 114 (1) ◽  
pp. 27-33 ◽  
Author(s):  
J. J. Hollkamp ◽  
S. M. Batill
Keyword(s):  
Time Series ◽  
Recursive Algorithm ◽  
Time Series Models ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Model Order ◽  
Identification Process ◽  
Truncated Svd ◽  
Value Decomposition ◽  
Norm Approximation

An identification method that uses order overspecified time-series models and a truncated singular value decomposition (SVD) solution is studied. The overspecified model reduces the effects of noise during the identification process, but produces extraneous modes. A backwards approach coupled with a minimum norm approximation, using a truncated SVD solution, enables the system modes to be distinguished from the extraneous modes of the model. Experimental data from a large flexible truss is used to study the effects of varying the truncation of the SVD solution and an order recursive algorithm is used to study the effects of model order. Results show that the SVD may be ineffective in separating the data into signal and noise subspaces. However solutions for highly overspecified model orders exhibit solution properties similar to the minimum norm solution and system and computational modes can be discriminated without a truncated solution.

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