Stable fuzzy-adaptive control using an introspective algorithm

In typical adaptive control using fuzzy function approximators, the centers of the decoding membership functions become adaptive parameters. As with any direct adaptive control, drift of adaptive parameters to large magnitudes can eventually lead to bursting behavior. Previous methods proposed for robust training utilize a mathematical modification of the update law, and may sacrifice significant performance to eliminate the risk of bursting. This paper proposes taking advantage of the local nature of fuzzy membership functions to design an introspective algorithm. At the moment the trajectory leaves a domain, the algorithm decides whether to keep the Lyapunov-stable adaptive update made during the domain activation, or discard it (depending on whether the error was decreased over the domain or not). The ability to account for large nonlinearities in a stable and high-performance manner is verified through an experiment with an underdamped flexible-joint robot.