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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.

This paper proposes an efficient approach for tuning L1 feedback filter of adaptive controller for multi-input multi-output (MIMO) systems. The feedback filter provides performance that trades off fast closed loop dynamics, robustness margin, and control signal range. Thus appropriate tuning of the filter's parameters is crucial to achieve optimal performance. For MIMO systems, the parameters tuning is challenging and requires a multi-objective performance indices to avoid instability. This paper proposes a fuzzy-based L1 feedback filter design tuned with multi-objective particle swarm optimization (MOPSO) to remove these bottlenecks. MOPSO guarantees the appropriate selection of the fuzzy membership functions. The proposed approach is validated using twin rotor MIMO system and simulation results demonstrate the efficacy of here proposed while preserving the system stabilizability., Comment: keywords Fuzzy logic control, multi-objective particle swarm optimization, estimate, L1 Adaptive control, fuzzy-L1 adaptive controller, Filter tuning, Fuzzy membership function tuning, pareto optimal front, optimal tuning, twin rotor MIMO system, Fuzzy membership function optimization, Robustness, Adaptation, multi-input multi-output, single-input single-output, PSO, FLC, MO-PSO