Conjugate gradient approach to blind separation of temporally correlated signals

2004 ◽  
Author(s):  
Liqing Zhang
Keyword(s):  
Conjugate Gradient ◽  
Blind Separation ◽  
Temporally Correlated ◽  
Gradient Approach ◽  
Correlated Signals

scholarly journals A New Projected Active Set Conjugate Gradient Approach for Taylor-Type Model Predictive Control: Application to Lower Limb Rehabilitation Robots With Passive and Active Rehabilitation

2020 ◽  
Vol 14 ◽  
Author(s):  
Tian Shi ◽  
Yantao Tian ◽  
Zhongbo Sun ◽  
Bangcheng Zhang ◽  
Zaixiang Pang ◽  
...  
Keyword(s):  
Predictive Control ◽  
Conjugate Gradient ◽  
Lower Limb ◽  
Numerical Approach ◽  
Active Set ◽  
Rehabilitation Robots ◽  
Active Rehabilitation ◽  
Limb Rehabilitation ◽  
Gradient Approach ◽  
Lower Limb Rehabilitation

In this paper, a three-order Taylor-type numerical differentiation formula is firstly utilized to linearize and discretize constrained conditions of model predictive control (MPC), which can be generalized from lower limb rehabilitation robots. Meanwhile, a new numerical approach that projected an active set conjugate gradient approach is proposed, analyzed, and investigated to solve MPC. This numerical approach not only incorporates both the active set and conjugate gradient approach but also utilizes a projective operator, which can guarantee that the equality constraints are always satisfied. Furthermore, rigorous proof of feasibility and global convergence also shows that the proposed approach can effectively solve MPC with equality and bound constraints. Finally, an echo state network (ESN) is established in simulations to realize intention recognition for human–machine interactive control and active rehabilitation training of lower-limb rehabilitation robots; simulation results are also reported and analyzed to substantiate that ESN can accurately identify motion intention, and the projected active set conjugate gradient approach is feasible and effective for lower-limb rehabilitation robot of MPC with passive and active rehabilitation training. This approach also ensures computational when disturbed by uncertainties in system.

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