Predictor-based control for an uncertain Euler-Lagrange system with input delay

Control of nonlinear systems with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. The problem becomes more difficult for systems with uncertain dynamics. In this paper, tracking controllers are developed for an Euler-Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. One controller is developed under the assumption that the inertia is known, and a second controller is developed when the inertia is unknown. For each case a predictor-like method is developed to address the time delay in the control input. Lyapunov-Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-global uniformly ultimately bounded tracking.