Constrained Multi-Agent Optimal Control for Football Tactical Decision Support: Analysis, Solver Verification, and Reproducible Scenario Experiments
Year: 2026
Type: preprint
Abstract: This work develops a constrained multi-agent optimal-control framework for football tactical planning, where player positions are modeled as states and admissible velocities as controls. A dimensionless Bolza functional combines territorial control, defensive exposure, compactness, pressing coverage, movement effort, and terminal formation accuracy. Existence of an optimal control is established, first-order optimality conditions are derived using Pontryagin’s Minimum Principle, and a time-discrete adjoint with an Armijo projected-gradient algorithm is employed for numerical solution. In a reproducible 11-player synthetic benchmark on a 105 × 68 m pitch, the optimized strategy reduces the objective from 0.20935 to 0.18511, corresponding to an 11.58% improvement over a feasible linear transition and a 38.26% improvement over the static compact baseline. All speed and pitch constraints are satisfied, while gradient verification and grid-refinement tests confirm numerical consistency. Priority experiments further reveal clear trade-offs between pressing intensity, defensive exposure, and movement effort. The proposed synthetic benchmark is intended to validate the mathematical and computational framework and provide a reproducible basis for future calibration with real tracking data.
Source: Research Square
Institution: Chouaib Doukkali University
Language: English
Subfield: Orthopedics and Sports Medicine
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W7207791006