Computational method for fractional-order optimal perimeter control with two-region urban traffic networks

Abstract Perimeter control—metering inter-regional flows so that vehicular accumulation is held at a target set-point—has emerged as a cornerstone macroscopic instrument for congestion relief in urban road networks. To endow the macroscopic flow dynamics with hereditary effects, we formulate a fractional-order dynamical system (FDS) whose non-integer differentiation orders and perimeter control strategy are simultaneously treated as unknown quantities governing the temporal evolution of regional vehicle accumulations. The central objective of this study is to identify these unknown quantities. To this end, a fractional-order optimal perimeter control problem (FOPCP) constrained by the FDS is formulated to minimize the total number of vehicles remaining within the urban road network. Subsequently, an explicit numerical scheme is devised to integrate the FDS, thereby transcribing the continuous-time FOPCP into a discrete-time FOPCP. Moreover, gradient formulas for the cost functional with respect to all decision variables are rigorously derived. A hybrid solution framework—based on model predictive control, gradient-based method, and a genetic search strategy—is proposed to numerically resolve the discrete-time FOPCP. Finally, comprehensive numerical experiments are furnished to corroborate the theoretical soundness and practical efficacy of the proposed algorithm.