Optimal control of coupled visitor-flow and energy dynamics in smart scenic areas: A differential-equation framework with IoT-based state estimation

  • Yue Wu orcid

    School of Hospitality, Tourism & Events, Taylor’s University, Subang Jaya 47500, Malaysia
  • Baijun Wu orcid

    School of Economics and Management, Jiangmen Polytechnic, Jiangmen 529000, China
  • Yingxuan Li

    School of Tourism and Hotel Management, Yunnan University of Finance and Economics, Kunming 650221, China
Article ID: 4677
DOI: https://doi.org/10.59400/adecp4677
Keywords: Pontryagin minimum principle; receding-horizon regulation; recursive feasibility; extended Kalman filtering; forward invariance; switching function; intermittent observations; neural symbolic derivation

Abstract

This paper develops a dynamic optimal-control framework for the coupled visitor-flow and energy-consumption processes of large-scale scenic destinations. Zone-level visitor density is modelled by nonlinear ordinary differential equations and facility loads by first-order linear equations with control inputs and occupancy disturbances, giving a single constrained plant for which we establish non-negativity, forward invariance of a compact set, and existence and uniqueness of solutions. For the associated finite-horizon problem, we prove that an optimal control exists and, applying Pontryagin's minimum principle, derive the costate equations and show that the optimal routing law is bang-bang with an explicit switching function. In contrast, the optimal energy law is saturated affine in the costate. A receding-horizon controller re-solves the problem online and, equipped with terminal ingredients, is recursively feasible and nominally asymptotically stable. An extended Kalman filter driven by an Internet of Things (IoT) sensor network supplies the state estimate, and its expected error covariance is proved uniformly bounded under Bernoulli sensor dropout. On a three-zone, nine-facility benchmark, the closed loop raises comfort compliance from 50% to 89% of slots, cuts mean waiting time by 57%, reduces total energy by 2.9% and load variance by 10%, and degrades gracefully at dropout rates up to 20%; a linear predictive variant proves competitive, so the nonlinear model's empirical advantage is not established. Robust stability under disturbance and distributed-parameter extensions remain open.

Published
2026-09-02
How to Cite
Wu, Y., Wu, B., & Li, Y. (2026). Optimal control of coupled visitor-flow and energy dynamics in smart scenic areas: A differential-equation framework with IoT-based state estimation. Advances in Differential Equations and Control Processes, 33(3). https://doi.org/10.59400/adecp4677
Issue
Vol. 33 No. 3 (2026): In Progress
Section
Article

Copyright (c) 2026 Yue Wu, Baijun Wu, Yingxuan Li

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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