Prescribed performance robust output regulation of uncertain Euler–Lagrange systems via self-learning mechanism

Abstract

This paper addresses the prescribed performance robust output regulation problem for Euler–Lagrange systems, where real-time reference signal information (such as position, velocity, and acceleration) is unavailable. We propose a control law that utilizes only the position tracking error and system velocity, while incorporating a self-learning mechanism for the reference signals. Additionally, two internal models are introduced to tackle the second-order dynamics of the Euler–Lagrange system, where the desired trajectory and disturbances are characterized by outputs of exosystems. These internal models reproduce the steady-state information, solving the trajectory tracking problem under uncertain system parameters. To ensure both steady-state and transient performance, we design a control strategy that guarantees that the output position error remains within a time-varying constraint function, while also ensuring that the error converges to zero asymptotically. This approach provides an effective solution to the robust output regulation problem with prescribed performance for Euler–Lagrange systems. Finally, the effectiveness of the proposed control strategy is demonstrated through comparative simulations.