Finite-Time Nonlinear <i> H _∞ </i> Control of Robot Manipulators With Prescribed Performance

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {H}_{\infty }}$ </tex-math></inline-formula> concept into the backstepping approach, using a novel virtual control, to guarantee practical finite-time convergence to a trajectory, whilst the closed-loop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\mathcal {L}_{2}}$ </tex-math></inline-formula> 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.