Prescribed time tracking control of constrained Euler–Lagrange systems: An adaptive proportional–integral solution

Most autonomous systems can be described by Euler-Lagrange (EL) model. This article investigates the problem of prescribed time tracking control for EL systems in the presence of modeling uncertainties, prescribed performance requirements and time-varying state constraints. Two proportional-integral (PI)-like control schemes with time-varying gains are developed with several favorable features: (1) achieving prescribed tracking precision within finite time in the presence of modeling uncertainties; (2) state constraints being obeyed all the time; (3) both the final tracking accuracy and the setting time being preassigned irrespective of initial condition or any other constraining parameter; and (4) bearing simple PI structure with analytical formula for robust-adaptive tuning gains, and demanding inexpensive online computation. The benefits and effectiveness of the proposed control are also validated via numerical simulation.