Preventing bursting in approximate-adaptive control when using local basis functions

Aiming to eliminate the bursting phenomena in low-gain approximate-adaptive controls that utilize local basis functions, this work proposes a new robust adaptation method. The bursting phenomena occurs when the approximatorʹs adaptive parameters (fuzzy centers or neural weights) drift to large values, eventually causing a sudden increase in state error. The existence of bursting often prevents universal approximators with local functions from controlling non-minimum phase systems, where bursting is associated with excitation of a natural frequency. The proposed solution adds two additional approximators to estimate each nonlinear function. One learns the output of the approximator used in the control signal. The other stores in memory the best weights found so far in the training. These parallel representations of the data guide the stable online training and prevent drift of the adaptive parameters. Simulation results with a generic nonlinear system illustrate the expected improvement in qualitative behavior over traditional robust methods leakage, e-modification, and deadzone when gains are restricted. An experiment with a planar two-link flexible-joint robot confirms the expected improvement in behavior, the new method prevents bursting without large sacrifice in performance.