Stabilization of strict-feedback nonlinear systems with input delay using closed-loop predictors

In this paper, we consider the control problem of strict-feedback nonlinear systems with time-varying inputand output delays. The approach is based on the usual observer/predictor/feedback approach, but thenovelty is the use of the closed-loop dynamics in the predictor. This approach allows to develop two designs,an instantaneous predictor and a delay differential equation-based predictor, that both attain the sameperformance in terms of system trajectories and input signal as in the case with no delays. The design basedon delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delaybounds. The resulting controller is much simpler to implement than classical infinite-dimensional predictors,and it is robust with respect to actuation and measurement disturbances. We illustrate the approach with anapplication to the control of a chaotic system with input delay.