Set-Membership Adaptive Robot Control With Deterministically Bounded Learning Gains

Abstract

As a powerful set-membership adaptive identification algorithm, the optimal bounded ellipsoid (OBE) enables fast convergence speeds because it exploits <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information about system dynamics by estimating sets of feasible solutions rather than single-point solutions. However, its learning gain matrix suffers from vanishing or unbounded growth, which seriously limits its practical performance. In this paper, a novel OBE algorithm is proposed to ensure that the learning gain matrix is constrained by upper and lower bounds, which are unaffected by the hardly predictable excitation levels and can be determined before implementing the algorithm. Thus, the system robustness and tracking capability for time-varying dynamics can be improved. In light of the proposed OBE identification algorithm, an adaptive robot control strategy is further proposed, where the robot dynamics are reconstructed through neural networks. The practical partial asymptotic stability of the closed-loop system is demonstrated using the Lyapunov method. Furthermore, noisy acceleration signals and the inversion of the inertial matrix are eliminated with the proposed control strategy. Experimental results on a robot manipulator validate the effectiveness of the proposed approach.