Finite-Time Nonlinear H∞ Control of Robot Manipulators With Prescribed Performance

This letter addresses the problem of robust finite-time tracking control with prescribed performance for robot manipulators experiencing uncertain inertia and external disturbance. We develop a control strategy that incorporates the nonlinear $\boldsymbol {\mathcal {H}_{\infty }}$ concept into the backstepping approach, using a novel virtual control, to guarantee practical finite-time convergence to a trajectory, whilst the closed-loop $\boldsymbol {\mathcal {L}_{2}}$ gain is less than a pre-specified value. We also use adaptive gains, instead of complex error transformations (common in prescribed performance controllers), to simultaneously impose constraints on the steady-state and transient response of the closed-loop, including maximum error, maximum overshoot, and minimum convergence rate. The developed controller is not contingent on solving the Hamilton-Jacobi or Riccati equations and is free of the singularities associated with using fractional power in finite-time control. The performance and efficacy of the proposed control framework are demonstrated through simulation studies and comparisons with pertinent works.