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<p>The accumulation-based macroscopic fundamental diagram framework is seldom used to characterize urban network traffic dynamics or to design perimeter controllers under uncertain probability distribution of traffic demand, despite the prevalence of such uncertainty in the real world. Therefore, a distributionally robust optimal perimeter controller for traffic networks under the worst-case probability distribution of traffic demand is highly desirable and of significant practical importance. Current literature lacks such a distributionally robust optimal perimeter controller for this specific problem. A primary hurdle has been the failure to adequately account for uncertainty in the probability distribution of traffic demand. In this paper, we consider the vehicle conservation equations within a nonlinear two regions macroscopic fundamental diagram continuous-time dynamical (N-TR-MFD-CTD) system, where the perimeter controller is unknown. The traffic demand is uncertain and is modeled as a stochastic vector with known upper and lower bounds and the first-order moment. The purpose of this paper is to determine this optimal perimeter controller under the assumption of a worst-case probability distribution for the traffic demand. We formulate a distributionally robust optimal perimeter control problem, structured as a bi-level optimal control problem governed by the N-TR-MFD-CTD system. This system is lifted to a higher dimensional linear system using the Koopman operator. To solve the bi-level optimal control problem, the duality theory is applied to transform it into a single-level optimal control problem with a non-smooth term. The non-smooth term is then approximated by a smooth function, and the convergence of the approximation is established. The model predictive control scheme, combined with a hybrid optimization algorithm is employed to compute a closed-loop solution through solving a series of online optimal perimeter control problems. The paper concludes with simulation results that demonstrate the effectiveness of the proposed approach.</p>

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Distributionally Robust Perimeter Control Approach for Two Regions Based on Koopman Operator

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Jinlong Yuan,
  • Chongyang Liu,
  • Kok Lay Teo,
  • Tao Zhou,
  • Kang Li,
  • Yuanyuan Li,
  • Kuikui Gao

摘要

The accumulation-based macroscopic fundamental diagram framework is seldom used to characterize urban network traffic dynamics or to design perimeter controllers under uncertain probability distribution of traffic demand, despite the prevalence of such uncertainty in the real world. Therefore, a distributionally robust optimal perimeter controller for traffic networks under the worst-case probability distribution of traffic demand is highly desirable and of significant practical importance. Current literature lacks such a distributionally robust optimal perimeter controller for this specific problem. A primary hurdle has been the failure to adequately account for uncertainty in the probability distribution of traffic demand. In this paper, we consider the vehicle conservation equations within a nonlinear two regions macroscopic fundamental diagram continuous-time dynamical (N-TR-MFD-CTD) system, where the perimeter controller is unknown. The traffic demand is uncertain and is modeled as a stochastic vector with known upper and lower bounds and the first-order moment. The purpose of this paper is to determine this optimal perimeter controller under the assumption of a worst-case probability distribution for the traffic demand. We formulate a distributionally robust optimal perimeter control problem, structured as a bi-level optimal control problem governed by the N-TR-MFD-CTD system. This system is lifted to a higher dimensional linear system using the Koopman operator. To solve the bi-level optimal control problem, the duality theory is applied to transform it into a single-level optimal control problem with a non-smooth term. The non-smooth term is then approximated by a smooth function, and the convergence of the approximation is established. The model predictive control scheme, combined with a hybrid optimization algorithm is employed to compute a closed-loop solution through solving a series of online optimal perimeter control problems. The paper concludes with simulation results that demonstrate the effectiveness of the proposed approach.