Optimal Control Design For Nonlinear Stochastic Systems With Input Delay

From a 2-Link 6-muscle arm model which includes input delay and random distur-bances, we introduce a class of nonlinear stochastic differential equation with control delay. A new stochastic control problem is proposed to achieve minimal energy con-sumption, and a method for locally-optimal control of this problem is presented in this paper. Firstly, we linearize the system dynamics and discretize the cost function in the vicinity of the trajectory x(t). which results from applying u(t) to the deterministic sys-tem x(t)= f(x(t),u(t), u(t-τ)). Secondly, through approximate expansion as the first order around (x(t), u(t)), our original optimal control problem is converted to a modified Linear-Quadratic-Gaussian (LQG) problem. Thirdly, using the dynamic programming principle, a locally-optimal control law is designed to obtain the optimal state trajectory. Finally, performance is demonstrated on a 2-link 6-muscle arm model.