The distributed discrete-time heterogeneous multi-agent optimization problem with unbounded position constraints and nonconvex velocity constraints was considered in this paper, where the models of agents are described by first- or second- order difference equations, the position constraints are assumed to be unbounded and convex and the velocity constraints are assumed to be bounded, closed and nonconvex. An improved distributed algorithm is adopted, under which, all agents could collaboratively minimize the entire objective function and the positions and velocities could always stay at the corresponding constraint sets. Then the convergence analysis is completed by the coordination transformation and the properties of projection operator and constraint operator. Finally, we give examples to illustrate the correctness of results.

本文考虑了具有无界位置约束和非凸速度约束的分布式离散时间异构多智能体优化问题，其中智能体模型由一阶或二阶差分方程描述，假设位置约束是无界的和凸和速度约束被假定为有界、封闭和非凸。采用改进的分布式算法，在该算法下，所有智能体可以协同最小化整个目标函数，并且位置和速度始终保持在相应的约束集上。然后通过协调变换以及投影算子和约束算子的性质完成收敛分析。最后，我们举例说明结果的正确性。