  L1 adaptive controller has been recognized for having a structure that allows
decoupling between robustness and adaption owing to the introduction of a low
pass filter with adjustable gain in the feedback loop. The trade-off between
performance, fast adaptation and robustness, is the main criteria when
selecting the structure or the coefficients of the filter. Several off-line
methods with varying levels of complexity exist to help finding bounds or
initial values for these coefficients. Such values may require further
refinement using trial-and-error procedures upon implementation. Subsequently,
these approaches suggest that once implemented these values are kept fixed
leading to sub-optimal performance in both speed of adaptation and robustness.
In this paper, a new practical approach based on fuzzy rules for online
continuous tuning of these coefficients is proposed. The fuzzy controller is
optimally tuned using Particle Swarm Optimization (PSO) taking into accounts
both the tracking error and the controller output signal range. The simulation
of several examples of systems with moderate to severe nonlinearities
demonstrate that the proposed approach offers improved control performance.
Keywords: Fuzzy logic control, single-objective, multi-objective particle swarm
optimization, L1 Adaptive control, fuzzy L1 adaptive controller, L1 fuzzy
adaptive control, L1 fuzzy adaptive controller, fuzzy L1 adaptive control,
Filter tuning, Fuzzy membership function tuning, optimal, optimal tuning, Fuzzy
membership function optimization, Robustness, Adaptation, multi-input
multi-output, single-input single-output, estimate, PSO, FLC, nonlinear,
adaptive, online, off-line, Fuzzy adaptive controller, Fuzzy adaptive control,
single input single output, multi input multi output, SISO, MIMO, robust,
uncertain, uncertain nonlinear system, disturbance, unknown, Adaptive Fuzzy
Control Design, stable.
