Distributed predefined-time optimal allocation for multi-target tracking using constrained kWTA networks

Distributed task allocation plays a crucial role in multi-target tracking, particularly in dynamic, large-scale environments. This paper investigates the optimal task allocation problem (TAP) for distributed multi-target tracking, where agents must be appropriately assigned to track multiple targets while avoiding conflicts and untracked targets. The TAP is formulated as a constrained k-winners-take-all (kWTA) problem by adopting the target-agent distance as the evaluation criterion. Since the constrained kWTA formulation imposes specific requirements on the input signals, the problem is categorized into consistency and inconsistency cases. For the consistency case, a distributed constrained kWTA network is developed to achieve predefined-time convergence to the optimal task allocation. For the inconsistency case, a distributed perturbation mechanism is designed to eliminate the inconsistency while preserving optimality. Numerical simulations demonstrate the effectiveness and scalability of the proposed networks, offering practical value for real-world dynamic multi-target tracking scenarios.