Distributed Fixed-time Optimization Control for Multi-agent Systems With Set Constraints
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摘要: 本文研究一类具有状态约束的多智能体系统优化控制问题, 提出了一种具有固定时间收敛特性的分布式优化控制算法. 该控制算法由局部投影模块、一致性模块和梯度模块构成, 其中局部投影模块确保智能体的状态在固定时间内收敛到局部约束集合, 基于时变增益的一致性模块实现所有智能体的状态在固定时间内收敛到一致值, 基于时变增益的梯度模块实现智能体的状态在固定时间内收敛到最优解. 利用凸优化理论和固定时间李雅普诺夫理论, 分析了算法的固定时间收敛特性. 算法收敛时间的上界值不依赖系统的初始条件, 因而可以根据任务需求来预先设计收敛时间. 最后通过数值仿真验证了理论结果的有效性.Abstract: This paper studies a class of optimization problem with local constraints for multi-agent systems, and a distributed optimization algorithm with fixed-time convergence is proposed. The proposed distributed controller consists of local projection module, consensus module and gradient module. The local projection module is used to ensure that the states converge to the local constraint set in the fixed time; the consensus module with time-varying gain guarantees the fixed-time state consensus; the gradient module with time-varying gain ensures the states converge to the optimal solution in fixed-time. The fixed-time convergence of the proposed algorithm is analyzed by using the convex optimization and the fixed-time Lyapunov theory. Since the upper bound of convergence time for the proposed algorithm does not depend on the initial condition, it possible to predesign the convergence time according to the task requirements. Finally, numerical simulations verify the effectiveness of the theoretical results.
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图 1 相同局部集合约束下优化问题(2)的仿真结果
Fig. 1 Simulation results for optimization problem (2) with a common constraint set
图 2 不同局部集合约束下优化问题(2)的仿真结果
Fig. 2 Simulation results for optimization problem (2) with nonidentical local constraint sets
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