Fuzzy Fractional-Order Adaptive Control for Mobility-as-a-Service Orchestration: A Cybernetic Approach

Mobility-as-a-Service (MaaS) orchestration faces critical challenges in managing the Service Quality Index (SQI), Fleet Utilization Ratio (FUR), and Dynamic Pricing Index (DPI) under uncertain and time-varying urban demand. Existing approaches—including multi-agent reinforcement learning (MARL) and hybrid learning-optimization methods—lack provable stability guarantees and systematic uncertainty handling, limiting their reliability for safety-critical urban mobility systems. This paper introduces the first control-theoretic framework for MaaS that simultaneously provides fractional-order modeling, complete fuzzy rule coverage, and Lyapunov-guaranteed stability. The proposed Fractional-Order Adaptive Fuzzy Controller (FOAFC) embodies Ashby’s Law of Requisite Variety through a dual mechanism: a proportional component that attenuates large-scale disturbances and provides global stability, and a complete 2,187-rule fuzzy inference system that amplifies fine-grained decision variety near the operating equilibrium—together matching controller complexity to the inherent variety of the MaaS operational envelope. Fractional-order Grünwald-Letnikov dynamics with differentiation orderq= 0.99 are employed to explicitly capture the hereditary memory effects of urban traffic flow, including long-range congestion propagation and demand correlation timescales of approximately 30 seconds, which integer-order models structurally fail to represent. Lyapunov stability is rigorously established using the Fractional Barbalat’s Lemma, providing asymptotic convergence guarantees despite parametric uncertainties and nonlinear system dynamics. Simulation results demonstrate 95.35% convergence to the target equilibrium—representing an optimal engineering tradeoff between tracking accuracy and stability, as gains beyond the critical valueK2= 195 cause complete system failure—alongside 95.7% RMSE reduction over classical PID and triple dominance over pure adaptive control across RMSE, settling time (53.4 s, 4.3% faster), and control energy (20,402 units, 1.1% lower). Near-perfect operational compliance is achieved: 100% SQI adherence, 99.3% FUR efficiency, and 100% DPI stability. Monte Carlo validation across 30 independent trials under ±20% initial condition variations and ±15% parameter perturbations yields a 100% success rate and coefficient of variation of 3.47%, confirming robust, production-ready performance. This work provides a mathematically rigorous and operationally viable foundation for next-generation urban mobility systems.