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Haohao Wu
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RESEARCH ARTICLE

Discrete stochastic optimal control for multi-stakeholder
governance of crop rotation and fallow insurance

Haohao Wu1* ,  Linbo He1 ,  Yuncheng Hu1* ,  Junhong He2
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1 College of Public Administration and Law, Hunan Agricultural University, Changsha, Hunan , China
2 School of Economics and Management, Wuhan University, Wuhan, Hubei , China
IJOCTA, 026330208 https://doi.org/10.36922/IJOCTA026330208
Received: 11 August 2026 | Revised: 24 August 2026 | Accepted: 25 August 2026 | Published online: 31 August 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Multi-stakeholder ecological governance requires coordinated decisions under environmental uncertainty, yet existing agricultural governance models rarely integrate stochastic disturbances, dynamic stakeholder controls, and policy constraints within a unified analytical framework. This paper develops a discrete-time stochastic optimal control framework with mixed constraints for multi-agent decision systems subject to bounded random disturbances. The framework is motivated by and applied to multi-stakeholder governance of crop rotation and fallow insurance, where soil fertility serves as the system state and stakeholder decisions form the control vector. The discrete-time Pontryagin Maximum Principle yields necessary optimality conditions and analytical control laws for all agent types, including a closed-form insurance compensation ratio. Stochastic Lyapunov analysis establishes finite-horizon practical bounded mean-square behavior under the constant control law. We further propose an error feedback control law u*f,t = clamp [1 + k ( S* − St ), 0, 1] that introduces a contraction term, transforming the error dynamics from an unbounded random walk to a stable first-order autoregressive process with bounded steady-state variance ; the optimal gain k = 1 / α yields a minimum bound of σ2. Monte Carlo simulation (10,000 trials) confirms a 68.0% reduction in trajectory standard deviation and a threshold violation rate decrease from 29.7% to 14.9%. Parameter calibration based on field survey data from 1,187 valid questionnaires across three provinces validates the theoretical model. The framework generalizes to similar multi-stakeholder ecological governance systems with stochastic disturbances.

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Funding
This work was supported in part by the Later-stage Funding Project of the National Social Science Fund of China under Grant No. 24FSHB019 (Research on Farmland Circulation Embedded in Three-Dimensional Structure), and in part by the Hunan Provincial Postgraduate Research and Innovation Project under Grant No. CX20251147 (Research on Object Determination, Mode Selection and Implementation Path of Cultivated Land Rotation and Fallow from the Perspective of Food Security).
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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