AUTHOR=Shi Tian , Tian Yantao , Sun Zhongbo , Zhang Bangcheng , Pang Zaixiang , Yu Junzhi , Zhang Xin 
  
TITLE=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
  
JOURNAL=Frontiers in Neurorobotics
  
VOLUME=Volume 14 - 2020
  
YEAR=2020
  
URL=https://www.frontiersin.org/journals/neurorobotics/articles/10.3389/fnbot.2020.559048
  
DOI=10.3389/fnbot.2020.559048
  
ISSN=1662-5218
  
ABSTRACT=In this paper, an echo state network (ESN) is firstly established to realize intention recognition
for human-machine interactive control of lower-limb rehabilitation robots. A three-order Taylor-type
numerical differentiation formula is 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 projecting active set conjugate gradient approach is
proposed, analyzed and investigated to solve MPC. This numerical approach not only incorporates
both active set and conjugate gradient approach, but also utilizes projective operator which can
guarantee that the equality constraints are always satisfied. Furthermore, a rigorous proof of
feasibility and global convergence also indicate that the proposed approach can effectively solve
MPC with equality and bound constraints. Finally, simulation results are 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.