Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems

Dai, Zhifeng

doi:10.1155/2014/921364

Cited by 5 publications

(3 citation statements)

References 33 publications

(36 reference statements)

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“…Under some suitable conditions, the global convergence was proved independent on the line search rules. Furthermore, the rate of convergence was improved by the algorithm …”

Section: Optimal Robust Controller and Finite‐time Stabilitymentioning

confidence: 99%

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

Sun

Tian

Wang

2017

Optim Control Appl Methods

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SummaryFor finite-time optimal robust control problem of bipedal walking robot, a class of global and feasible projected Fletcher-Reeves conjugate gradient approach is proposed based on an online convex optimization algorithm. The optimal robust controllers are solved by projected Fletcher-Reeves conjugate gradient approach.The approach can rapidly converge to a stable gait cycle by selecting an initial gait. Under some suitable conditions, we provide a rigorous proof of global convergence and well-defined properties for projected Fletcher-Reeves conjugate gradient approach. To demonstrate the effectiveness of the bipedal walking robot, we will conduct numerical simulations on the model of 3-link robot with nonlinear, impulsive, and underactuated dynamics. Furthermore, to indicate the availability of high-dimensional robotic system, the main result is illustrated on a nonlinear impulsive model of a bipedal walking robot through simulations via finite-time optimal robust controller. Numerical results show that the projected Fletcher-Reeves conjugate gradient approach is feasible and effective for bipedal walking robots. Therefore, it is reasonable to infer that the optimal robust control approach can be used in practical systems.

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“…Under some suitable conditions, the global convergence was proved independent on the line search rules. Furthermore, the rate of convergence was improved by the algorithm …”

Section: Optimal Robust Controller and Finite‐time Stabilitymentioning

confidence: 99%

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

Sun

Tian

Wang

2017

Optim Control Appl Methods

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“…It is demonstrated that the active set

can be seen as the equality constraints of (7), and according to Rosen's gradient projection method (Rosen, 1960 ; Dai, 2014 ), an active set projection matrix is given as follows:…”

Section: Projected Active Set Conjugate Gradient Algorithm For Nonmentioning

confidence: 99%

“…Some modified conjugate gradient methods, which consider the constrained conditions, were thus proposed by modifying the search direction and a projected operator (Dai, 2014 ; Sun et al, 2018 ). Besides, a projected gradient method, which projected the gradient into the feasible region, was proposed by Rosen ( 1960 ), and some modified conjugate gradient methods were extended by some researchers based on the mentioned methods (Li and Li, 2013 ; Dai, 2014 ). Those modified conjugate gradient methods were also applied in optimal robust controllers and robots (Sun et al, 2018 ).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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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A Rapidly Convergent Projected Hestenes-Stiefel Conjugate Gradient Algorithm for Optimal Robust Controller of Bipedal Walking Robots

Sun

Lian

Liu

et al. 2018

2018 IEEE 8th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER)

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Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems

Cited by 5 publications

References 33 publications

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

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

A Rapidly Convergent Projected Hestenes-Stiefel Conjugate Gradient Algorithm for Optimal Robust Controller of Bipedal Walking Robots

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