Premium
A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots
Author(s) -
Sun Zhongbo,
Tian Yantao,
Wang Jing
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2339
Subject(s) - control theory (sociology) , conjugate gradient method , robot , controller (irrigation) , nonlinear system , convergence (economics) , computer science , nonlinear conjugate gradient method , gait , robust control , optimal control , underactuation , mathematical optimization , mathematics , artificial intelligence , artificial neural network , control (management) , gradient descent , physiology , physics , quantum mechanics , agronomy , economics , biology , economic growth
Summary For 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.