Prediction Control for Nonlinear Systems with Stochastic Input Delay

Abstract

This chapter focuses on nonlinear systems with a stochastic input delay, which can arise from communication lags for instance. For input-delay systems, the use of prediction-based control methods is quite standard. This method was first used for constant delays before being extended to time-varying delays. Yet, the design of a prediction-based controller to handle stochastic delays is still an open problem. In this chapter, we propose to describe the stochastic input delay as a continuous-time Markov process with a finite number of values. This random delay is then robustly compensated through a constant-horizon state prediction. Applying the method of backstepping, we obtain that exponential stabilization of the closed-loop system is achieved, under a sufficient condition. This condition bears on the range of the possible values of the time lag, which should be sufficiently small and close enough to the prediction horizon.