Control of an input delayed uncertain nonlinear system with adaptive delay estimation

Abstract

A partial differential equation (PDE) based controller is developed for a nonlinear system with bounded external disturbances and unknown time-varying input delay. Motivated by predictor-based delay compensation methods, a linear transformation is used to map the time-varying input to a control input which varies both in time and space. This technique separates the delay magnitude and derivative terms, and gives added flexibility of control gain selection over traditional robust control methods. Unlike existing literature on predictor-based controllers, which inherently depend on system dynamics, an auxiliary error signal is defined which does not require exact model knowledge. Further, a nonlinear mapping is used to map the non-compact time domain to a compact spatial domain, and then a neural network (NN) is used to estimate the unknown time-varying input delay. A Lyapunov-Krasovskii functional is used to prove uniform ultimately bounded tracking. Simulation results validate the controller performance for an Euler-Lagrange system with unknown input delay.