Control of an Uncertain Euler-Lagrange System with Known Time-Varying Input Delay: A PDE-Based Approach

A partial differential equation-based tracking controller is developed for a class of uncertain nonlinear systems with bounded external disturbances and time-varying input delay. A novel robust controller is designed such that the control input varies with both time and a spatial variable. The designed controller features gains to compensate for the delay and delay derivative independently and further robustness is achieved since the controller does not require exact model knowledge. A novel Lyapunov-Krasovskii functional is used in the Lyapunov-based stability analysis to prove uniform ultimate boundedness of the error signals. Numerical simulation results illustrate the performance of the proposed robust controller.