A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots

Abstract

In this article, combined rapidly exponential control Lyapunov function with hybrid zero dynamics, a sufficiently descent projected Dai–Yuan approach is proposed, investigated, and analyzed for online solving optimal robust control problems with linear equation constraints of bipedal robots. Moreover, a new approach is developed for designing optimal robust controller. To demonstrate the effectiveness and feasibility of the proposed method, we will conduct numerical simulations on the model of three-link robot with nonlinear, impulsive, and under-actuated dynamics. Numerical results show that the bipedal robot can walk effectively and stability on the ground though the optimal robust controller when the parameters of the hybrid system model are disturbed three times. Furthermore, under the random noise condition, the bipedal robot can walk stably and effectively through online computing the nonlinear optimization problem for optimal robust controller. In addition, some classical control methods are compared with the developed approach in this article, numerical results are reported and analyzed to substantiate the feasibility and superiority of the proposed method for linear equation constrained optimization problem. Last, this article develops a systematic approach on exploiting optimal robust control technique to design hybrid system models for robustly and accurately via online solving linear equation constrained optimization problems.