Lyapunov recursive design of robust adaptive tracking control with L-2-gain performance for electrically-driven robot manipulators

This paper develops a new Lyapunov recursive design for the tracking contro l problem of rigid-link electrically-driven robot manipulators with uncerta inty by taking a tracking performance into account. The tracking performanc e is evaluated by L-2-gain from a torque level disturbance signal to a pena lty signal for the tracking error between outputs of the manipulator and de sired trajectories. The novelty of our approach is in the strategy to const ruct such a Lyapunov function recursively that ensures not only stability o f a tracking error system but also an L-2-gain constraint, which provides a closed-form solution for non-linear H-infinity control problem without usi ng a Hamilton-Jacobi inequality. Two controllers, i.e. robust and robust ad aptive control laws with L-2-gain performance, are designed such that the c losed-loop error system is globally stable in the sense of uniform ultimate bounded stability with the L-2-gain less than any given small level. Exper imental works are carried out for a two-link electrically-driven manipulato r. Experimental results show an enhanced tracking performance of the propos ed control scheme.