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 input and output delays. The approach is based on the usual observer/predictor/feedback approach, but the novelty 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 same performance in terms of system trajectories and input signal as in the case with no delays. The design based on delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delay bounds. 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 an application to the control of a chaotic system with input delay.